I think you need help even in framing your question. The cognitive, affective, and conative processes in schizophrenia are very complex. When I was doing my clinical internship in the 1970s, there were two books that really helped unpack schizophrenia for me. One was Irving Weiner's Psychodiagnosis in Schizophrenia whichoffered definitions and descriptions of a variety of psychological processes operating in schizophrenia. The second was Silvano Arietie's The Interpretation of Schizophrenia. If nothing else, these books  make clear how many layers there are to the neurological processes that might underlie schizophrenia. Another layer appears when you look at how communication patterns of family members induce a kind of craziness. Thus, The Pragmatics of Human Communication byPaul Watzlawick and others can help illuminate various "schizophrenic" communication patterns, as can Watzlawick's How Real is Real? Also very helpful is Jay Haley's essay on "the art of being schizophrenic" in The Power Tactics of Jesus Christ and Other Essays. I recommend all these "heavy" books because you cannot frame the neurological question without first understanding how the thought processes should be described. And then you raise a separate question, which is that of the nature of delusions. You may find the following article helpful: 

Psychosis, delusions and the “jumping to conclusions” reasoning bias: A systematic review and meta-analysis.

doi: http://dx.doi.org/10.1093/schbul/sbv150

By Dudley, Robert; Taylor, Peter; Wickham, Sophie; Hutton, Paul

Schizophrenia Bulletin, Vol 42(3), May 2016, 652-665.

We did a systematic review and meta-analysis to investigate the magnitude and specificity of the “jumping to conclusions” (JTC) bias in psychosis and delusions. We examined the extent to which people with psychosis, and people with delusions specifically, required less information before making decisions. We examined (1) the average amount of information required to make a decision and (2) numbers who demonstrated an extreme JTC bias, as assessed by the “beads task.” We compared people with psychosis to people with and without nonpsychotic mental health problems, and people with psychosis with and without delusions. We examined whether reduced data-gathering was associated with increased delusion severity. We identified 55 relevant studies, and acquired previously unpublished data from 16 authors. People with psychosis required significantly less information to make decisions than healthy individuals (k = 33, N = 1935, g = −0.53, 95% CI −0.69, −0.36) and those with nonpsychotic mental health problems (k = 13, N = 667, g = −0.58, 95% CI −0.80, −0.35). The odds of extreme responding in psychosis were between 4 and 6 times higher than the odds of extreme responding by healthy participants and participants with nonpsychotic mental health problems. The JTC bias was linked to a greater probability of delusion occurrence in psychosis (k = 14, N = 770, OR 1.52, 95% CI 1.12, 2.05). There was a trend-level inverse association between data-gathering and delusion severity (k = 18; N = 794; r = −.09, 95% CI −0.21, 0.03). Hence, nonaffective psychosis is characterized by a hasty decision-making style, which is linked to an increased probability of delusions. (PsycINFO Database Record (c) 2016 APA, all rights reserved)

"Intuition is paranoia's slave".  Well said.    In a practical sense, we all have ideas, beliefs, that we hold onto, and are not open to critical thinking.  Or, open to critical thinking but not emotional change.  We have a deep attachment to the meanings of these ideas, beliefs, etc because it feels like they help us.  Who would give that up easily?

One interesting possibility is that people with paranoia gathe information in a biased way. Thus, for instance, paying special attention to certain types of actual evidence (e.g., gazes from other people) may lead to other biases (e.g., memory biases or jumping to conlcusion biases). So, gathering data in a biased manner may lead to handle information in a particular way that may, in turn, lead to other biases.

We showed this effect using a covariation task some time ago:

 Díez-Alegría, C., Vázquez, C., y Hernández, M.J. (2008). Covariation assessment for neutral and emotional verbal stimuli in paranoid delusions. British Journal of Clinical Psychology, 47, 427-437.

Although some of the answers to this post have directly addressed a specific disorder, (schizophrenia), this specific perspective can be a bit deceiving and can lack of a more accurate understanding of psychopathology, in general, in my opinion. Paranoia can be a symptom of any mental disorder, as well as being found in people, who wouldn't classify as having a psychopathology.  Like every other human behaviour or way of thinking, paranoia and many other symptoms that are prominent in certain mental disorders, may be present in every people to some extent. Every named condition, (such as paranoia, anxiety, delusions, hallucinations, paranoid delusions, depression, attention deficiency, obsessive thoughts, compulsory behaviour etc. etc.,)  has a spectrum of magnitude attached to it in the means of, frequency of the recurring thoughts and behaviour, how much distress it causes the individual subjectively, and how much it effects the social life of the individual. It should be emphasized that there are certain criteria like the ones I just listed, to classify a behaviour or thought as crossing over to a psychopathological threshold.  

So to address the question, I am interpreting that you are asking, why someone would have a paranoid thought, despite contrary 'evidence', that disprove that thought.  Although the answer to that can vary from case to case and from individual to individual, I can suggest from personal experience,that the mind of a deeply paranoid person is usually quite confused, not knowing whether to trust, what the majority of people call 'reality'.  Subjective reality and its conflict with thoughts, that are classified as the norm and normal way of thinking, can be a problem for most of us, humans, to a certain extent.  It is important to understand that what we classify as psychopathological behaviour is simply an OVER-deviation from the norm (i.e. from the majority's usual way of thinking and behaving).  And the trick in understanding paranoia and many other thinking ways that would be classified as 'deviant' is, that they are not alien feelings, that we cannot connect to. They just make some people's lives harder because they recur more in magnitude in that individual.  

So, long story short, you can look inside you for the answer to that question. When have you last felt not being sure of something, or a certain person's behaviour or objective or not trusted the person?.. I, myself feel it and question it on a daily basis with a lot of stuff. So, from a personal point of view, what makes a person 'paranoid' (quoting your way of putting it) can simply be the high frequency of the occurrence of those paranoid thoughts, which later get the individual more and more confused, resulting in social avoidance and even more paranoia, and so on.  It is a really complicated topic, and it has to be taken seriously, I think. I can send some articles, and empirical evidence(?) supporting a theory written about the basics and reasons(?) of paranoia and paranoia- related mental disorders, later, if you'd like. But this is just a start I guess, in a more subjective way. :)

Thank you for your detailed response, Pazar . I would like to read the articles you are going to send to me.

Clinical paranoia is a complex phenomenon which is probably predisposed/triggered by multiple biological and psychosocial factors. First, individuals with paranoia (or other psychotic symptoms) have been shown to have a heightened sense of aberrant salience, finding some 'irrelevant stimuli' attention grabbing and self-relevant (see Shitij Kapur's work). They are distressed by this sense of salience and are driven to make sense of them using top-down appraisals. When they do that, they are prone to cognitive biases such as jumping to conclusions, attention bias, and confirmatory bias (see Philippa Garety's and Steffen Moritz's work). Some of these biases have been shown to be stable predisposing traits (e.g. JTC bias, see our papers as well as Mahesh Menon, Matthew Broome, Philippa Garety, Emmanuelle Peters etc). Some say that patients have affect-related cognitive biases such as interpersonal over-sensitivity and negativistic self schema in the background as well (see David Fowler and Paul Bebbington). Once they establish the paranoid thinking, some are able to give them up if they have belief flexibility, whereas others stick to the beliefs due to inflexibility, cognitive rigidity, or a still high sense of aberrant salience (see treatment trials that target cognitive biases that maintain paranoia thinking or delusions in general; e.g. Steffen Moritz, Helen Waller, Daniel Freeman).

You can access some of our papers relevant to this topic below:

https://scholar.google.com.hk/citations?user=DgcHCz8AAAAJ&hl=en

Happy researching!

Many studies has suggested that there is a cognitive error existed with paranoid ie Jumping to conclusion & impairment of cognitive insight ie ability of openness of feedback and flexibility in thinking, so that one can accept and ready to adapt the opinions of others for his/ her benefit.  This might be one significant reason of not being able to derive a right conclusion and hold to it despite of disconfirming evidence.

Hemsley gives another point of view, based in cognitive psichology, in wich schizophrenic patients are better reasoners than normal ones, because they are more flexible when it is about disconfirm hypothesis once they have lost certain abilities to take advantage of regularities, patters based in experience (schemes I mean). So, they are lost in a world in wich they cannot stablish connections between stimuli at the same level than the other people, but, this casuses that they are continuosly looking for patters, which finally causes that sometimes their connections are weird and atypical (could this explain than certain ideas sound so strange??).  

Do we ned to consider  interpersonal theory of self or even self psychological insights!

Here's another, broader research paper contributing to the understanding the concept of 'paranoia' in general. It 'investigates the structure of paranoia in a 'non-clinical' [or undesignated] population'

http://bjp.rcpsych.org/content/bjprcpsych/186/5/427.full.pdf

You can go and check the link for the whole research paper.  I have found it to be a nice and a beneficial one in understanding a variety of concepts around the topic...

Here's the Abstract:

BACKGROUND:

Previous studies of paranoia have assessed only limited numbers of paranoid thoughts, and have not considered the experience from a multidimensional perspective or examined the relationship between different suspicious thoughts.

AIMS:

To assess a wide range of paranoid thoughts multidimensionally and examine their distribution, to identify the associated coping strategies and to examine social-cognitive processes and paranoia.

METHOD:

Six questionnaire assessments were completed by 1202 individuals using the internet.

RESULTS:

Paranoid thoughts occurred regularly in approximately a third of the group. Increasing endorsement of paranoid thoughts was characterised by the recruitment of rarer and odder ideas. Higher levels of paranoia were associated with emotional and avoidant coping, less use of rational and detached coping, negative attitudes to emotional expression, submissive behaviours and lower social rank.

CONCLUSIONS:

Suspiciousness is common and there may be a hierarchical arrangement of such thoughts that builds on common emotional concerns.

http://bjp.rcpsych.org/content/186/5/427.long