There are numerous theories of intelligence. One of the most contested points across different theories is the question of whether intelligence is a single, general construct or a system of multiple domain-specific constructs. Also, if there are multiple kinds of intelligence, how many are there and what do they consist of?
Debate over this question goes back over 100 years. On the one hand you have theorists like Charles Spearman who argue that intelligence is a general cognitive construct. That is, there are not different kinds of intelligence. Rather, there is only one singular, foundational mental capacity that underlies all activities requiring intelligence.
On the other hand, you have theorists like Thurstone, Cattell, Gardner, Sternberg, who propose that intelligence is not singular, but multidimensional or admits of multiple forms. These thinkers differ quite a bit in their characterizations of intelligence, but this question is about Howard Gardner, so let's stick with him:
Gardner proposed a theory of 7 multiple intelligences, respectively: linguistic, logical-mathematical, spatial, musical, bodily-kinesthetic, interpersonal, and intrapersonal (he later speculated an additional 3 kinds: naturalistic, spiritual, and existential). In support of his theory, Gardner pointed to various sources of evidence:
1. Potential isolation by brain damage - the faculty can be destroyed, or spared in isolation, by brain injury.
2. Existence of exceptional individuals such as savants - the faculty is uniquely spared in the midst of general intellectual mediocrity.
3. Identifiable core operations - the faculty relies upon one or more basic information-processing operations.
4. Distinctive developmental history - the faculty possesses an identifiable developmental history, perhaps including critical periods and milestones.
5. Evolutionary plausibility - admittedly speculative, a faculty should have evolutionary antecedents shared with other organisms.
6. Support from experimental psychology - the faculty emerges in laboratory studies in cognitive psychology.
7. Support from psychometric findings - the faculty reveals itself in measurement studies and is susceptible to psychometric measurement.
8. Susceptibility to symbol encoding - the faculty can be communicated via symbols including (but not limited to) language, picturing, and mathematics.
* A major limitation with Gardner's evidence is that it is primarily theoretical, not data-driven. In other words, it has intuitive appeal, but there is very little to no data that supports the existence of these multiple, independent kinds of intelligence. This is the major criticism of Gardner's view.
Now, to answer the question directly. To my mind, a myth is an account that is demonstrably false. That is not the case with theories of multiple intelligences, including Gardner's. Rather, there is a lack of supporting data for the theory - which is quite different. So, to call it a 'myth' is a bit strong. However, educators are right to be skeptical about the notion of multiple intelligences - at least, until there is more data (i.e., evidence) to support the idea.
Sources
Gregory, R. J. (2007). Psychological testing: History, principles, and applications (5th ed.). Pearson: Boston, MA.
Gardner argues that there is a wide range of cognitive abilities and there is only a very weak correlation between them. For example, the theory predicts that a child who learns multiplication easily is not necessarily smarter than a child who has great difficulty learning the process. A child who takes more time to master simple multiplication: 1) can better learn multiplication through a different approach; 2) can excel in areas of activity outside of mathematics; or 3) perhaps even looks at understanding the multiplication process on a fundamentally deeper level, or perhaps as a completely different process. Such a fundamentally deeper understanding can lead to what looks like slowness, but in fact it can hide mathematical intelligence, potentially higher than that of a child who quickly memorizes the multiplication table, despite a less in-depth understanding of the multiplication process as such.
Traditional tests of intelligence in psychometrics tend to show high correlations between different tasks and aspects of intelligence, rather than the low correlation predicted by Gardner's theory. Nevertheless, many educators support the practical value of the approaches proposed by the theory
(1) In this context, what does it mean to ask whether it is a "myth?" I think you need to define that first before you ask your question. What are you actually asking? That would be helpful and very useful.