Why is it so hard for men to apologize to their women?

My wife and I had it out the other day and we pretty know how to push eachother's buttons and we just went ahead and let it all out anyway. I said some hurtful things to her and she said some hurtful things back. I knew that I should have apologized, but for some reason I just could not bring myself to it. I knew that once I did apologize it would smash all the beef that had been cooked up between us. But for the most part I just flat out refused and just felt like that all I had to do was hold out and make her apologize and from there it would be all good. In the meantime I feel that we really went about 12 steps back from all of the recovery that we made since stopping the proceeds to our divorce over a year ago. Now I find myself sleeping on the couch and thinking about things that I shouldn't. We haven't said two words to eachother all day long and we both just interact with the children and don't coomunicate. We are at the phase of having silent arguments and not working with the children together, but on our own terms; which does nothing but confuse the kids. I outright refuse to eat any of her cooking in protest due to the ongoing dilemma and I know that I'm hungry, so I eat when she isn't looking. I am at the point where I feel that there is just no point in all of this nonsense so I think I will apologize tomorrow and get back to life as normal.