Why is professor Xavier bald ?

It's the way he was drawn.
I'm sure that
originally
it was probably intended to make him appear "professorial" - i.e. older and intelligent and big-headed (i.e. big-brained).

Also: it was probably intended to emphasize that he had mental super powers.

Later
much later
it was revealed that he was a relatively young fellow
(despite having been in WWII - yeah, Marvel always had trouble explaining the WWII heroes still being young-ish superheroes in the 60s...and 70s...and 80s...)

Eventually the comics gave an explanation as to why such a young fellow had no hair. Apparently his mental powers were SO powerful that it affected his hair, causing it to fall out...

Which begs the question: why didn't any of the other super-mental-powered people go bald? Like Mastermind and Marvel Girl? I guess they just didn't have the necessary mental "oomph" to knock their own hair out...

Because every time he uses his powers, his hair spikes up and turns Super Saiyan so he shaves his head to hide he's using his powers. But as Charlie Fox said, he's old. I've seen some people lose their hairs in their 30s.

He's old, and shaves his head. In the movie Logan, he has some hair.