Bi-variate analysis (cross tab) can not show the right association .In multivariate logistic regression the impact of confounding factors can be controlled so that the effect can be oppositely different from the bi-variate analysis (cross tab).

The logistic regression has few weakness, one of this weakness is the relation confusion, give you A positive B value and at the same time Exp(B) < 1< or the opposite.

One important think to be aware of about generalized linear regression is that you deal with partial correlations, which is a bit subtle to think about.

You can use this toy exemple to think about it:

In a study on children, knowlage about their age may give you quite good information on the level of their skills: for instance, older children may have greater ability in sport and music.

You can also imagine that if some children spend more time playing football they will spend less time studying music. Now if you want to check the correlation between the ability to play football and the ability to play music in children you will certainly find a faire good positive correlation between those skills. Now introduce the age in your linear model and you will find out that you have a negative association between the ability to practice sport and music.

Now be carefull, I am not saying that there is no correlation between the ability to play football and the ability to play music ! The correlation you seasured exist and it is valide ! You just find out that both variables may be explained by a third one wich is the age of children. This is also known as the common cause.

Also, it's not because there is no causality, or event worse, inverse causality between sport skill and musik skill in children that you don't have a good information. If you know that a children cannot catch a ball you can be pretty sure that is is very young and that he would not play piano like Mozart. This kind of indirect information is often use in medical reaserch where some easely measurable variables may be used as surrogate markers of a disease even is there is no causality between the measured variable and the disease.

Contrary to what has been mentionned in previous answer, this is not a statistical problem or weakness of the generalized linear model (GLM) including the logistic regression but simply a matter of good interpretation of GLM results and what you are realy doing when using it. Also Bi-variate (cross tab) always gives you the right association, again it tells nothing about causality but by definition an association is an association no more no less. The job a the statistician is to find out the good interpretation and what it really means.

Best,

Marc