Having a language argument with my guy, I say “how do you mean?” And he says “what do you mean?” When we dont understand eachother. Is one more right than the other?

They're both right. “What” is more common but I hear “How” too. Plus “how” gives the impression that you understood but you just need more context. I like that it feels less aggressive.
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In English it's “what do you mean”. With “how do you mean” I get what you're trying to say, but sounds off and may be a direct translation from another language, which makes it sound correct to you
I get that you all want to be anti-prescriptivist, but let's be helpful to OP here — in the vast majority of English dialects, “how do you mean” sounds terribly awkward on its own. “What do you mean” is the correct answer here.
Nope. Not at all. “How do you mean” has a distinctly different meaning. As /u/eriksealander said, it's softer. It's like saying “I'm sure you're right, but I don't get how you came to that conclusion”.
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“What do you mean” would come up in a context where you're challenging a person (although not exclusively), while “how do you mean” never would. It's also why how is less common, it's not as versatile, but if it's the meaning you want, it avoids possible misunderstandings. The variation “How do you figure?” is in between the two, it implies some skepticism, whereas “How do you mean?” doesn't, while still not being an active challenge of what was said.
They mean the same thing in general. In fact, I used to be a “what” person, but now use “how”. In one sense, using “how” sounds (to my ear) a little more formal and educated. And “how” has among its subtle meanings “in what way” or “by what manner”, while “what” is the object of the meaning, the specific thing meant. Using “what” points to a specific object of the meaning, using “how” more implies the overall condition of the meaning.
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Probably Engilsh is a second language for this person. Prepositions are a big source of errors, even for natives.

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