The idea that men have more power in our society is a myth, that oppresses both sexes. We don't. We never have.
Recite to any typical male any part of the feminist litany (men are rapists, men cause all the wars, men are child-molesters, men are wife-beaters, men are violent criminals ...), and he will often just nod in acknowledgement and say something like, "Yeah, men are bastards, aren't they?". Notice that it's "they", not "we". Individual men know that they personally do not fit feminist descriptions of manhood, but are so alienated from other men that they can easilty assume there is some vast, amorphous mass of men somewhere "out there" that does fit the stereotypes.
Because a large proportion of those who hold visible power (eg. apparent economic and political power) are men, it is easy for a man who is fully aware that he is not a part of that group, to hear criticism of "men" in those roles and not realize that it refers to him, as if the speaker were implicitly adding a qualifier ("all men except for Keith here"). He remains unaware that the speaker holds him in contempt, and holds him all the more in contempt because he is sitting there smiling and nodding as if he were not the one under discussion. The male newsreader who smirks as he reads stories about men being blamed for their childrens' poor eating habits, and laws in Switzerland to punish men for not sharing the housework equally, is a prime example.
Some men may also feel that, by agreeing that men don't count as fully human, they improve their own attractiveness to women by comparison - the "All Men are Bastards Except for Me" syndrome. They may even be successful in the short term, but in the long term, they only contribute to the dehumanising and devaluing of all men, and the emotional warping of boys who constantly hear that what they are growing up into is something to be ashamed of.
Chivalry was basically the protection of women at the expense of men. Now that it is rarely necessary to protect women from danger, many still feel that it is the job of men to protect women from everything, including the consequences of and responsibility for their own actions. Women who commit crimes cast themselves as the victim, and society bends over backwards to find excuses for them, rather than admit that they could be responsible for a criminal act. Courtship practices in the west invariably involve the man taking all the emotional risks, especially the first approach; the part a woman plays in letting him know his approach is welcome, is practised in a way that allows her to deny it later if things don't work out: "I was just being friendly, and he sexually harassed/seduced me."
Not all women are opposed to mens' rights, and not all of those opposed to mens' rights are women. It is probably fair to say that feminists are one enemy; "feminists" includes such groups as Men Against Sexual Assault (MASA) and Men Against Patriarchy, as well as womens' or wimmins' groups. MASA actively campaigns against the activities of the Mens' Rights Agency in Brisbane, and has recently even won funding for its efforts.
Of course, not even all feminists are opposed to mens' rights. Warren Farrell broadly divides feminism into two schools of thought: Adolescent Feminism, which blames men for all the evils of the world and assumes that all men are rapists, child molesters, and active conspirators in the "patriarchy"; and Adult Feminism, which believes that both men and women are oppressed by traditional gender roles, and that men are willing and able to make changes complementary to those made by women through the womens' movement. Farrells' terms are potentially misleading, as they imply that one is a more mature form of the other, or that Adult came later than Adolescent feminism.
Christina Hoff-Sommers expresses the same distinction as Gender-Feminism versus Equity-Feminism. The latter is the assumption that women and men are entitled to equal or equivalent rights, and must consequently assume equal or equivalent responsibilities. It is typified by the original suffragettes, and most of those who campaigned for equal political and economic rights for women up until about the sixties or seventies. Gender feminism is the more modern brand of feminism, and the brand that has produced womens' studies, the concept of patriarchy, and the myth of universal male power. Modern women who say "I'm in favor of equal rights for women, but I'm not a feminist", are distancing themselves from Gender feminism, even as they declare their belief in the basic tenet of Equity feminism.
Christine Jackman of the Courier Mail has written of men being "stunned into silence by the cogency of feminisms' arguments". It would be more accurate to compare the silence of men in the face of early (Equity) feminism, with the sullen silence of a man required to shuffle across a bus or train seat to make room for a fat woman to sit next to him. Even though it may be personally inconvenient, for all our grumblings, we recognise the change as only fair and just. And remember, the analogy is not true of all men. There were men (and women) who were determined not to allow women the vote, or the right to own property, or any of a wide range of rights, usually under the assumption that they were protecting women. Similarly, the womens' movement would never have happened without supportive and sympathetic males, such as the husbands of the original suffragettes, and especially the male legislators who voted to extend rights to women. The stirrings of the mens' movement in response to modern (Gender) feminism are equivalent to the protests of our man in the bus seat who, having moved over, now finds that the woman is demanding he stand so that she can have some elbow-room.