First of all, great that you seem to have a relatively equal situation. It reads like your wife is actually working. Good for you.
However, your accusation is totally wrong and uncalled for. I know the name, but I have never read/heard anything from the Tate brothers. In fact, my opinion about female priviledge in our society stems purely from my own experience, in particular my mother. This is something I'd like to have (make and female) feminists understand. All I need to be resentful of female priviledge is my own mother and her spite and her totally lack of humility. Much of backlash towards feminism is self-inflicted. We don't need hateful men to tell us what to think about female priviledge. All we need is our own eyes. Not all women are shining examples of rationality and empathy. Maybe feminists should start by working on/with the bad apples in their own circles.
Fact is, my mother owns way more then I do, despite actually only having worked roughly 5 years in her whole life. All she owns was built up by men in the family of my father. And she inherited everything, including the priviledge of not having to go to work. If I could, I'd step into her shoes every day. And she doesnt even realize her priviledge, which is insulting.
This is just one example of the elderly spitting on the young, sometimes without even noticing. This tension is going to increase in the future even more.