I have the urge to understand what's going on so even if my correct opinion is being challenged I do try to understand why someone, especially my partner, is seeing it differently. Usually, I come up with a more or less reasonable conclusion and then I do kind of apologise as I can see their/her point of view (usually, I would not accept it, although this really depends on the person. Some are almost as often right about things as I am). Hence, I'm often the one that apologises. When it comes to stronger arguments and smaller fights, I'm usually the person who apologises because whatever the reason - I don't want to see her suffer.
This can also be a problem, though. Directly or indirectly, I have been told a few times that some girls would prefer me to be a bit more resistant when it comes to disagreements but I don't really see a point (except for 'acting manly'). I always try to convince others of my opinion if they oppose it or if I'm being asked to do so but only up to a certain point. If they cannot understand my reasoning or appear to not wanting to understand it, I stop - what else could I do?
I rather have a problem with it the other way around: I'm getting annoyed when (potential) girlfriends just agree with me although they clearly have a different opinion - just for the sake of not having a disagreement. What the heck, I want a partner I can respect and not a trophy to show around...