Whether or not you agree on transgender issues, Twitter emailed Peterson and showed him in their terms of service where it says no misgendering and no dead naming.
So they showed him exactly which rule he broke and he still is acting like he doesn't know what he did wrong he did a long rant about it on YouTube and he honestly seems to be a little mentally unhinged.
Also, you agree to these terms and conditions when you create your Twitter account
I agree with you on this point. If you disagree with the rules of Twitter then why did you agree to them when you opened the account?
If you realize now that you made a mistake and you don't agree with their rules the fault is not with them, it is with you. You need to pack your bags, shake off the dust and leave.
Now on his side of the coin it may be that he has had that account for a long time and this rule may have been added after he first opened the account. I don't know the answer to that, don't know when he opened the account, don't know when this rule was made. In that case it does seem unfair that someone can build up a Twitter account with a Twitter following and to have this be a very important part of your business and then change the rules on them. I'm not saying that is what happened, simply saying that before you can judge Peterson we should be able to let him tell his side of the story first. Generally speaking you would have people grandfathered in. Otherwise if Peterson is forced to leave Twitter because of a rule they created after he opened the account I think he has a case for a lawsuit over breach of contract.
For example several months ago I entered into a lease agreement for a car. However, the car was not available. I paid them $1,000 and waited for several months. I picked up the car yesterday. During those three months interest rates on loans have changed dramatically. If they changed the details of our agreement it would be a breach of contract. You can't change my contract which I made with you three months ago because you now have a new interest rate.