// No matter what Clare says, 'haitch' is incorrect - it may be widely used, but it's wrong. //
It's better, I think, to say that "aitch" is *standard*, rather than *correct*. The former is merely an acknowledgement of what's normally used, or normally indicated in dictionaries, but the latter implies a judgement that really amounts to a question of what "wrong" even means in languages.
(a) Presumably you'd intend to point to a dictionary, but this is problematic: which one? Both dictionaries I have in my house only give "aitch", and don't even acknowledge "haitch" as existing, let alone wrong, but it can be found in a couple of more obscure and all-encompassing resources. (Note that my Collins only gives "barth" for "bath", and not the Northern pronunciation of "baff", again showing that just because it's not in a dictionary doesn't mean it's wrong).
(b) even still, dictionaries are generally not seen as prescriptive, whether the authors intend it to be or not, and besides it's usual that they only record the received pronunciation rather than any/all dialects.
(c) As debated in, for example,
https://www.independent.co.uk/news/long_reads/haitch-or-aitch-pronunciation-letter-h-old-english-a8393766.html , "haitch" is arguably the more historical pronunciation. In itself, that doesn't entirely matter (just because one was "correct" centuries ago doesn't mean it's "correct" today), but does serve to show yet again that language is constantly changing both over time and across social classes and regions (or even religions).
"Haitch" is seen as standard in, among others, Australian English, Hiberno-English.
(d) As for the continued evolution, it seems that "haitch" is increasingly popular, and it may well be only a couple more generations before "aitch" is regarded as a mere historical relic.