Your teacher is mostly correct. While it’s true that some British speakers drop the H more frequently than Americans do, the true is that all native speakers *unconsciously* drop the H in unstressed position. If you go to the Merriam-Webster dictionary, you’ll see the pronunciation listed thus: \ (h)iz, ˌhiz \ The pronunciation given first shows the optional H. The Oxford Learner’s Dictionary also shows both pronunciations (first the stressed, then the unstressed): /hɪz/, /ɪz/ So unless the word “his” is at the beginning of a phrase or is being emphasized, it will usually be pronounced without the H. The way you talk is the way you listen, so if you expect us to pronounce the H in “his”, you’ll be sadly disappointed most of the time (this will hurt your comprehension). Also, the Arabic H tends to be much stronger than the English H, so you will you sound unnecessarily foreign.

I think it depends on dialects. For example the queen’s English and what you’d see on the BBC news for example would probably pronounce the “h” in “his”. I don’t know if it is technically “correct” English to drop the “h” sound (I would tell you to pronounce the “h” if you were doing a speaking exam or job interview) but it’s very common in everyday colloquial speech, as least in some parts of the UK - I pronounce “his” and “is” the same most of the time.

Like the sister Adalet mentioned, the dropping of the “h” sound may be due to the teacher’s own dialect. There is a brother from Ivory Coast whose conversation language is French and he tends to drop all the “h” sounds that are the beginning of words. So “hospital” becomes “ospital”

Not correct for U.S. English - - we generally pronounce the H's as the beginning of words. Except honor and honest (English is a crazy language).

We pronounce the word 'his' with a clear h sound here in the US. You can try the Cambridge Dictionary website and listen to the pronunciation of both 'his' and 'is' in standard American English and standard British English.