I used to be one of those people that was always "sorry", and apologizing at every turn, to the point that people complained about it. I'm more selective now about where and when I apologize, consider whether my behavior and the situation really warrant it, what the value of the apology might be to the other person and most importantly that it actually has the potential to help. (When I do it though, I do it right; no fake apologies, a.k.a. the non-apology apology.)

What I read from this article though, "Refusing to apologize can have psychological benefits (and we issue no mea culpa for this research finding)" in the European Journal of Social Psychology (Okimoto, T.G., Wenzel, M. and Hedrick, K., 2012), may offer some insight into why some might not apologize much or at all:

Despite an understanding of the perception and consequences of apologies for their recipients, little is known about the consequences of interpersonal apologies, or their denial, for the offending actor. In two empirical studies, we examined the unexplored psychological consequences that follow from a harm-doer’s explicit refusal to apologize. Results showed that the act of refusing to apologize resulted in greater self-esteem than not refusing to apologize. Moreover, apology refusal also resulted in increased feelings of power/control and value integrity, both of which mediated the effect of refusal on self-esteem. These findings point to potential barriers to victim–offender reconciliation after an interpersonal harm, highlighting the need to better understand the psychology of harm-doers and their defensive behavior for self-focused motives.

I suppose those who've likewise noticed this to be true would need to see an inherent value in making an apology, and their ability to ascribe a positive value to the action could vary quite a bit.