A straightforward journalistic article from the Atlantic that does a decent job of explaining how and why learning styles theories simply don't work, with a particular focus on VARK. The takeaways are that, yes, people do often prefer to learn in different ways but, no, accommodating their preferences has no effect on comprehension or recall, and, even if it did, it would be doing a disservice to learners to do so because life ain't like that (with darker implications of teaching people to believe they need something they don't, thereby actually reducing their capacity to learn). We've known this for a really long time. I am still shocked that (at least as recently as 5 years ago) up to 90% of teachers actually believe in the learning styles myth. Of all the people that should know better, teachers are pretty much at the top of the list.

The article points to a good range of recent reliable sources, including:

Another Nail in the Coffin for Learning Styles? Disparities among Undergraduate Anatomy Students’ Study Strategies, Class Performance, and Reported VARK Learning Styles

Learning style, judgements of learning, and learning of verbal and visual information.

The Scientific Status of Learning Styles Theories

Matching Learning Style to Instructional Method: Effects on Comprehension

Proviso: there's nothing wrong, and everything right, about thinking of different ways to enable people to learn stuff, and learning styles theories all encourage people to do that. As a design tool, that serves as a reminder that there is seldom one best way to teach anything, I'm all in favour of anything that gets the creative juices flowing and that allows learning designers to take and apply different perspectives. This is the sort of thing that increases engagement, interest, and time on task. Even if it is barking mad or positively evil, as long as we don't let on why we are doing it, any way we find to do this is probably fine. I could, for instance, imagine ways that a 'men are from Mars, women are from Venus' perspective could, despite the very unsavoury nonsense behind it, actually result in some diverse approaches to teaching that would benefit everyone, as long as we didn't try to teach men one way and women another, of course, and as long as we didn't let on that we had designed it with these thoughts in mind. Substitute whatever demographic divide, bias, bigotry, or preference you like - religion, weight, politics, sexuality, race, drinking habits, liking for cats or dogs, general level of fitness, whatever. As long as you keep it to yourself and only let it affect how you design your teaching, then do what works for you. There's a slippery slope to be avoided here, and some complexities to be wary of, especially when it changes the content and intended outcomes - if, say, you chose religion as your discriminator, that does not mean you should teach both evolution and intelligent design, though there might be value in remembering that there might be a religious demographic that won't readily accept any amount of evidence or argument, so you might want to think about how best to help them, just as you should think about how best to help people with any disability.  Let's just keep it that way, though - a dirty little in-house secret about how we design our teaching by thinking (wrongly or not) about differences between our learners -  and stop inflicting the stupid notion on our students.