Men often have arguments like that-- explosions and then all is forgiven-- women, not so much-- much more kept inside and then festers. Italians (written as a pure blood LOL) get it all out in the open -- In both Italians and males (and if you are dealing with Italian males--Oh, Sweet Madonna!!) catharsis occurs and so both parties can move on.
Where things get sticky is not the external volatility, it is the emphasis on preserving "face." To say "I was wrong" or "I am terribly sorry" is to risk losing face. Of course, the paradox is that the more one is concerned about preserving face the less one has to begin with. The secure, strong person has no problem apologizing because the essence of who she or he is does not get compromised by the apology.
So the next time you get frustrated that the other person refuses to apologize (or maybe it is you who should...) remember it is because of basic insecurity. That may make the situation easier to handle.