"Why is the threat of withdrawal affection often used to prevent men from speaking up for their rights?"
Because we live in a society where girls have their self esteem plumped up by society, and whilst boys are groomed to see themselves as disposable.
Seriously, there's a reason that t-shirts and books didn't come out saying "Girls Are Stupid Throw Rocks At Them." There's a reason, when Jeff Foxworthy decided to do a bit about beautiful babies and ugly babies, the beautiful baby happened to be his daughter, and the ugly baby happened to be a "friend's" son! There's a reason that film and TV shows depict boys/men without girls/women as unhappy, or boys/men who take girls/women for granted as being filled with regret...
...and that reason seems to be because society has groomed men to be kept in line by women first and foremost...and barring that, by the state.
So is it any wonder that shaming language is a key tool in the arsenal of women who try to discourage men from views, opinions and values that run afoul of anything questioning the superiority of women and the inferiority of men?
"Why would any man even want to be with a woman who wont let him speak up for his rights, and tries to silence him by shaming him?"
Because those men have been conditioned to believe that women are the keys to happiness, and not siding with women on issues like feminism...is a quick, easy way to lose that "happiness."
Of course how happy are those same men if they are one of the roughly 40% of men who marry, who end up getting dumped by their wives, and losing most of their material possessions, as well as regular access to their kids? Because after all, in a Western world where more than half of all marriages end in divorce, and women file for divorce anywhere from 70-80% of the time, there's around a 40% chance that if you're married man, you're going to at some point be a divorced man.