To be serious, I'd say that every day is international men's day because as men we are better paid, better educated and do not have to put in '110% to prove that we're as good as other men'
To be UNserious, the label in the link is funny, because it ironic (if a man really DID give all his washing to his wife/girlfriend, it's fairly certain he'll spend the rest of the week wearing dirty clothes).
What should men be fighting for? One thing that springs to mind is an equalisation of divorce laws. If a man who is worth £10m marries a woman who divorces him after a year, why should she be entitled to half is wealth? And why should he pay alimony until she marries again?
I know that this is the case where poor men marry rich women (I'm looking at YOU Madonna), but in reality, that's quite rare.