What did he do that you feel he should say he's sorry?

I don't think that's a "man" thing, I think it's a sign of someone's character. Admitting when they're wrong, or are responsible for hurting you could be a red flag of many things. Off the top of my head perhaps stubbornness, defense mechanism, self absorbed. etc.

Some people are also not shown empathy and lack the ability to show it.

Is this a person you have a relationship with? Your bf or husband? Has he always been this way? This is something that is not healthy and very selfish. In fact in order for you two to be healthy (because this will effect you as well) then it's something that needs to be addressed.

Sometimes people genuinely don't believe they are wrong. If they don't believe they're wrong, they won't apologize.

I used to think this was a "woman thing" but as I aged I realized it was a "woman I tend to attract thing"

In my experience it is a sign of extreme insecurity or a sign of a projected abusive personality. Either of those will not often admit wrong doing, both so that they do not appear weak.

My narcissistic x husband rarely apologized, and if he did, it was a manipulation tactic. He could not admit that he was wrong. These types can somehow twist things so that YOU end up apologizing to them for their emotionally abusive and bad behavior. If you are in a relationship with a man who can't offer a sincere apology when warranted, this is a huge red flag.

Some people just suck.

Nope! I'm sorry! There, that was easy.

I agree with stillbitterjaded. Saying sorry when you admit to yourself that you were wrong, is not that difficult. The hard part, for some, is admitting that they were wrong. I have never had a problem apologizing because I tend to be honest with myself and am not so ego driven that I can't look at myself objectively. If I'm wrong, I apologize ... easy as that.