First off, get a new gynecologist. Yours sounds like a complete jerk. I've never heard of a hard or soft hymen before, but it sounds like you might have a micro-perforated hymen instead, where the hole in the hymen is extremely small. This can cause extreme pain when inserting a tampon or having penetrative sex.
Micro-perforated hymen can be fixed by either practicing and working your way up slowly (to bigger sizes, in order to slowly stretch the hymen), which can be painful, or having surgery done to create a normal-sized hole.
But seriously, get a new gynecologist.
I would think a doctor could safely break it. Good luck
Let me clarify. As in surgically. It is very unusual to have this kind if difficulty that sex does not break the hymen.