When men are the ones who go around hitting on women
They did a study of approaches at social gatherings (bars, clubs, social gathering spots), and found that 80% of interactions were intiated by the woman...the guy may have done the approach, but only after the woman gave some sort of signal that he may approach.
fighting with each other to win over a woman
Err - the nature of 'fighting' is quite different. From what I've seen, many more women part ways with their women friends over guys than the other way around.
'Fighting' happens on both sides - is there a point to this?
why is marriage considered to be the happy ending of women's lives
You might have to clarify what this question has to do with the previous two statements. After all, if you don't want that type of guy, don't marry that type of guy.