It’s a harmony-vs.-truth thing.
Middle-class women are socialized to maintain relationships and keep the peace, even if this requires occasional insincerity. Men of all classes are socialized to be relatively more confrontational and are encouraged to be forthright, even if this results in open disagreement. Both sexes are taught to own up to their mistakes, so as far as sincere apologies are concerned, women are not socialized to be more apologetic in that sense.
It’s a more/less thing, not a strict categorical difference. The same dynamic can be observed when comparing cultures: some are more likely to favor maintaining harmony at the expense of honesty than others.
I’ve known women who ended every expression of their opinion or knowledge with a giggle. (“If we want to get this project done by the deadline, we’ll have to work on it this weekend, hee hee.”) Frequent insincere or unnecessary apologies are the same kind of behavior.
On the other hand, being taught to present one’s opinions in a way that doesn’t step on other people’s toes can be an advantage when one works in large organizations, which may be one of many reasons why women are gaining ground in the corporate world and academe.