POWER, pure and simple. Women and men view conflict differently. Women, in general, seek resolution and argue and raise voices to be heard and to get to a resolution. Women view apologies as a gesture to acknowledge feelings and repair hurt feelings.
Men, certainly not all, but some view an argument as a win-lose situation and they're in that primordial fight-flight mode and they're going for a win. Many men, especially from Western cultures, don't process their feelings as rapidly as women, and thus lash out to protect their ego, which has come under attack. They view apologies as a sign of weakness or as a concession that the other party was "wrong." They feel that they are admitting defeat by apologizing, which doesn't help resolve conflict.
However, when men do cool down, they usually can discuss and resolve the issue while women may hold onto the emotions of the conflict longer.
These are generalizations and certainly do not apply universally to everyone or every situation.
Men are From Mars, Women are From Venus