I could look at graduation rates and see that males are graduating at a much lower rate than females in my university. Should I favor men in order to even the odds? Of course not. Even though some of the worst students I have had are white males...
I had two students dominate, or at least predominate, my two classes last semester. One was an African American male, the other was a white female. I didn't try to shut them down, but I did make sure that they weren't the only people speaking.
I have Latino students who speak better Spanish. They are at an advantage, since class is only in Spanish. Should I call on the more because they are more oppressed, or less because they are comparatively advantaged in this particular situation?
There isn't some huge competition to participate. Many students, the majority in fact, don't want to say anything at all. I'll still make them say something from time to time, but I want to be a professor, not a dentist.
Should I call more on students who do not seem as gender normative? So I am supposed to make a judgment about someone based on their external mannerisms? Their skin color? Their last name? Should I favor Asian over whites, or vice-versa? How should I treat Jews? International students? Should I ask for students' or parents' tax returns to see how well off they are?
If my students knew I was calling on them more or less based on their race / gender / perceived gender identity, would they like it? Yes, you seem like you're gay, so I'll call on you more than the guy sitting next to you. Wouldn't then the straight white guy with an invisible disability make his own claim? To announce that you were going to do this would be disastrous. The woman who tweeted that she would call on white males only "if she had to" is practicing overt discrimination. Of course the right wing picked up on it, but that does not make it right. Sometimes seemingly progressive ideas are simply terrible.