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It is unclear from this man's letter whether he wants to solve the root problems that are making the women around him irate, or whether he just wants the women to stop being shrill and irritable. If it is the former case, then bully for him. It warms my heart when men actually step up to the plate and ask how they can help fight the battles that feminists have had to fight alone for so long.
If it is the latter case, well, sorry dude, but sometimes women have genuine grounds for complaint. You cite Broadsheet for sniping. Don't you think that's just a little dismissive of the important issues that blog brings up? You say that a lot of women are really angry. Yes some complaints and angry t-shirts contribute unduly to the hosility between the sexes, but there are also people who have real reasons for being angry. I would rather have a more cantankerous society and allow the righteous complaints to come to the surface than to have everybody just "chill out" and have those complaints get buried in the name of peace.