Great question. There are actually two different English vowel sounds that often get confused.
The vowel in man is /æ/ (the same vowel as in cat, hat, and apple). Arabic doesn't have an exact equivalent to /æ/, so native Arabic speakers usually approximate it with fatḥa /a/. That's close enough to be understood, but it isn't identical.
The schwa (/ə/) is a different sound altogether. It's the relaxed, unstressed vowel you hear in words like about, banana, and the second syllable of problem. Arabic also doesn't have a true equivalent of /ə/. When Arabic speakers pronounce it, they typically substitute a short a, i, or u, depending on their dialect or how they interpret the spelling.
So, if your question is specifically about man, the closest Arabic approximation is a fatḥa, even though it won't sound exactly like an American English /æ/. If you're asking about the schwa (/ə/), there really isn't a direct Arabic equivalent, and it's best to think of it as a separate English vowel that has to be learned on its own.