"What's the matter with that guy? Doesn't he respect women?"
Most of the time, when I hear that line, the woman saying it is using the word "respect" when she really means "venerate."
Once upon a time there was a trade-off under which women earned special treatment. It was contingent on eschewing rough behaviors like heavy drinking, fighting, and sexual promiscuity. Women were presumed morally superior, and expected to live up to that. They were presumed gentler than men, and expected to live up to that, as well. Even feminine aesthetics were about being something more special than a man, which is why women were and still are allowed the luxury of wearing clothing that restricts one's ability to perform heavy or hard labor. In return for living up to those standards, women were entitled to certain concessions not afforded to men. They could display more delicate sensibilities such as offense at rough language or crude subject matter, and expect their aversions to be indulged. They could expect exemption from some of life's responsibilities, like supporting a family or even themselves. It was not just a gentleman's responsibility, but his honor to assist a woman in need, and doing harm to a woman was taboo for any man. Women who lived up to the moral and social standards associated with their traditional role were considered respectable in a way that deserved veneration; men who lived up to theirs revered them.
The reverence that women today so loudly and crassly demand in the name of "respect" is not earned under such an arrangement. Sixty years of feminist protesting has freed women from the constraints of social obligation, allowing us to, without expecting judgement for it, become as crass, as violent, and as sexually promiscuous as men, and in many cases, more. Feminists fought for this under the guise of equality, demanding society acknowledge not only equality of rights and human value but capability and toughness. Feminists fought to free women from our side of the bargain, yet what do we hear from them the moment a man's equal treatment of a woman means she is no longer indulged or exempted as before? "What's wrong with that guy? Doesn't he respect women?"
What does that have to do with #gamergate? Well, it began with women complaining of a lack of equal treatment and ended up with a massive shaming campaign wherein women and their supporters drew on traditionally unequal standards to try to shame gamers into giving them special treatment; exempting the women central to the controversy from criticism they would be expected to face and address if they were men. Both the women and the media substituted a demand for veneration of women, requiring subjugation of male gamers' concerns, where an open dialogue was needed.
How is that respect for anyone?
You can see the same treatment in various issues discussed by the men's rights community. Bring up equal parenting rights, and women's groups shout down arguments in favor by demonizing fathers without evidence, calling them deadbeats and abusers. Try to apply fact and reason to discussion about the wage gap, and the misogyny card is immediately thrown down. In the face of impending equal treatment, women's groups defend gender disparity in likelihood of arrest, in chance of a conviction, in criminal sentencing, and in length and type of sentence served in cases where men and women commit the same crimes. Even in an area that should be a no-brainer, involuntary underage genital cutting, women's groups defend girls' bodily autonomy, demanding total elimination of the tradition, while supporting the use of it on infant boys. This, with no better reason than those given for the use of it on girls.
The same groups which claim physical equality in their arguments for equal pay reverse themselves when the discussion turns to intimate partner and sexual violence. Abuse is abuse, unless a woman is the perpetrator and a man is the victim. A man must treat a woman the same as he would another man... unless she assaults him. Then, he owes her the special treatment of not defending himself as he would against another man. She is to be coddled like an unruly child. Though we're equal when women's advocates are demanding an equal share of life's rewards (*edit - excellent point made by Bernard Chapin - feminists demand rewards women have not earned such as equal representation in CEO positions despite women not putting in the work and making the sacrifices to get there... a more than equal share*), when confronting life's rough side, we're not at all equal. Suddenly, women are inferior, not only too weak to back up their display of temper with a strong assault, but also too stupid to acknowledge that by keeping their fists to themselves. Which message should women buy into? Are we strong and smart enough to earn the same pay as roughnecks and loggers, scientists and engineers, or are we too weak to defend ourselves yet too stupid to refrain from picking fights with men anyway? Do feminists and other social justice warriors think women aren't savvy enough to notice that contradiction?
This indicates to me that women's outrage is badly misdirected. It isn't men's attitudes that need to be examined, but those of feminists and other social justice warriors who play the misogyny card to deflect attempts to hold women to the same standards and expectations faced by men. That behavior is not indicative of very much faith in their supposed charges.
Hey, feminists and SJWs! What's wrong with you guys! Don't you respect women?