Whoever has made a mistake should apologies first, but in relationships understanding other means a lot and if you understand your partner you may not need to apologies for your mistakes your kisses, hugs, feelings, emotions says it all.
yeah, I think quarrels are part of a relationship.
In our case...my bf would usually be the one to ask for apology, even if sometimes its my fault. hehe. But of course, if its really MY fault...then I'll apologize first.