TL;DR: Don't hit each other and show some goddamn respect and common courtesy to everyone.
This is a hard topic for me because like most dudes my mom raised me with the "never hit a woman" mentality and I have that embedded in my psyche. It's to the point where I used to let this one chick punch me in the shoulders and head when I was a kid (when I was 10-14ish) because I literally believed that I should never hit a women under any circumstances.
I still believe that but as I've grown it's not because I see women as weak but because at this point I feel like that respect should be afforded to every person. You shouldn't hit someone unless it's your last resort and it's because you're already being physically attacked or your safety is being threatened in a way that only violence can solve which is very few times. I'm more of a talk out the problems kind of person but with that I've digressed. Anyway it's hard for me to speak about it because I had that mentality before and I know what the person is thinking but even that is a form of sexism because it's a prejudice based on you thinking or feeling that women are weak.
I'm all for equality but what I don't understand is that there are women who say they are for equality one hundred percent but if push comes to shove a building is on fire, or a boat is sinking the first words they'd speak would be "
women and children first." I know there are many many women who believe in true equality not just "women should be treated better" but instead "everyone should be treated the same" and those are the kinds of people I relate to. I don't believe women should be treated better simply because they are women (same with men, they shouldn't be treated better simply because they're men) well at least not anymore (used to think never hit a woman always treat them with respect etc because it was something my mom always told me and always tried to make a point) and I regret that I used to have that mentality. I believe everyone be they man or woman should be treated the same. You should be able to speak to a woman the same way you would speak to a man and not be accused of being misogynistic for it. Saying there are things you can say to a man that you cannot say to a woman is separating the genders socially which is what equality is actually against that's however just my opinion.
I don't think a man should be able to hit a woman but on the other hand I feel that a woman shouldn't be able to hit a man and a man shouldn't be able to hit a man and a woman shouldn't be able to hit another woman. (That was a mouthful

) I feel this way because everyone should be able to speak honestly and openly without feeling like they could be attacked for it but they have to realize they need to afford the same right to the other person and allow the other person to speak their peace at least until things become more heated or out of control then at that point someone needs to leave the situation.
Something I also believe in is that the person who is being targeted needs to always try to leave the situation or find help if needed. This might sound stupid but I don't think someone should put up with unneeded bullshit and I myself will leave a real life conversation if the other person becomes loud or irate. I'm not going to put up with being yelled at if I'm not yelling at you that's simply respect something everyone should have for the person they're speaking to unless they've done something to lose that respect however even then they shouldn't be yelling and should simply leave the situation instead of sticking around to change the person's point of view (because at that point it's obviously not going to happen.) I don't know much about the Ray Rice situation as I don't get into sports all like that but I don't think his wife had the right to spit on him and hit him around however instead of hitting her back and reinforcing that behavior (ie her hitting him; because hitting her back pretty much says "it's okay for us to hit each other",) he should have removed himself from the situation even if that meant getting off of the elevator (think he was in an elevator) at the wrong floor and simply walking away. I don't think this because she was a woman but because as I stated I feel no one has the right to harm another person physically unless they feel that there is no recourse which honestly if he could have gotten off the elevator and removed himself from the situation there was recourse.
As for the first situation it seems it's always been like that. I might be overstepping myself but I feel woman aren't treated equally in situations like that because the mentality is "woman are weak" which is simply wrong. Both parties should have been dealt with in the same manner because they both used physical violence in a situation where there was no call for it. There are men that do that all the time with their gfs, wives etc and they're wrong for it but there are also woman that do that with their bfs, and their husbands and they're just as wrong for using verbal threats, intimidation and violence against another person.
Edit: Missed the n'ts on a few shouldn'ts >_< it's what I get for typing fast and not proof reading.