There is no logical argument against feminism that doesn't harbor lingering misogynistic viewpoints and ideologies. As a man, I can not fully attest to what it's like to live in America and around the world as a woman. However, what I can do, is recognize my privilege, which many fail to do.
As someone who defines themselves as a feminist, I take particular issue with women who do not. In most arguments I've seen, women against feminism cite extremism and religion as their reasons. In any case, these arguments choose to ignore the heart and core of what it is to be a feminist. The goal of feminism is to achieve political, economic, and social equality for the sexes. In any movement, there are extremists. Citing an extremist as a reason to condemn a movement demonstrates shallowness and an unwillingness to understand and interpret the movement for what it is.
Other women choose religion or their personal goals as fuel for their dismissiveness of feminism. A recent article on Odyssey expressed the opinion that It is okay to stay at home and be with your children, and to allow your husband to provide. That is obviously okay, and few feminists would disagree with that. What is not okay, is using your personal goals of homemaking as an excuse. If that's what you want for yourself, power to you. But you should recognize that there are millions of women who do not want to to occupy that role, and that are taking to the streets to fight the lingering misogynistic view points of the past. It's not appropriate to use your personal life and your religion as an excuse to not support the feminist movement.
Support your fellow women as they support you, as the ultimate goal of feminism is to create a society where women can be whatever they want, unrestricted by the misogynistic undertones of our society. Those core values of feminism support all women in all of their pursuits, including the stay at home mom, who know one should disrespect.