Anti-feminism is one example of misogyny. It is not the only example of misogyny but it certainly is an example of misogyny.
Looking at a different issue might help. There are those who insist that they are not racist, that they have black friends as a common piece of evidence that they are not racist. What they mean is that they like black people who don't make trouble, who are employed but not at levels higher than white people, that they are educated but not above their stations, that they don't do something so bold as to buy in the wrong neighborhood or attend the wrong school or attend a school where ANY white (preferably male) student was denied admission. That they do not express anything other than gratitude for being allowed to participate in white society to whatever extent that white society allows them to participate. They should not marry white women or have mixed babies. Preferably they should only have similarly docile, obedient, compliant children, no more than two and none of whom should have any physical or intellectual disabilities and of course no mental illnesses because let's face it: white people have enough problems acknowledging and coping with mental illness of nice white people. Above all, black people should not ever, ever appear angry or dissatisfied. They should not grow taller than the average white child for their age nor appear more sexually developed than the average white child for their age. They are allowed to be musicians, and athletes as well as domestic and physical labor workers. They can be actors in some limited roles that are written specifically for black people. They should always remember their place and not aspire to teach in white schools or to become doctors, lawyers, POTUS, or writers or politicians. Those jobs should be left to their betters. Feel free to substitute whatever racial demographic you would like, making whatever small changes necessary. Asians can be engineers and maybe scientists and professors, for example. Or violinists or pianists if they stick to classical music. I'm not sure what Hispanics are allowed to be aside from working in the restaurant industry, agriculture or some construction jobs.. This kind of not racist is perfectly happy to accept people of any race so long as they don't make them uncomfortable in any way, shape or form.
Or: Gay people are fine so long as they don't want to marry each other or have children with each other or live next door.
Anti-feminists are exactly this kind of not misogynists.