It's so confusing.
There's stereotypes about bickering, teasing, quarreling couples: basically, that all their arguments and so on are just the other side of the coin of their (intense) love for each other; that (verbal) fighting is just their way of flirting.
This manga plays on that idea and, in typical manga/anime-fashion, does so by doing it over the top and turning "argumentative bickering" into physically fighting each other and (non-serious) attempts of killing the love interest.
(if you want to see the same thing done to even greater extend check out LOVE/DEATH)