The right question

He didn't " put her into her place " he responded to something she said

I'm pretty sure she didn't start a conversation with him.

But she did post it publicly, which means it's open to responses. Just like how the guest made a comment and I can respond to them, like I did to them and you did to me.

Yes, but you're not supposed to, unless you really want to. Piers Morgan - for whatever reason - has a reputation as TV journalist, and when he engaged in a twitter fight with that children books author about her political views, that was already awkward, but hey, why not. But now this getting all sarcastic at a professional buttocks owner for being a little too poetic as a mother, that's desperate.

" you're not supposed to "
That's the whole point of Twitter, though. You talk to other people. If you just want to update people on stuff make a blog and turn off comments, a social media site where the purpose is to interact isn't the place to go if you want no one to talk about your posts.

But it's optional. You choose who you answer and why. And I'm criticizing his choices. Am I not supposed to?

And getting onto Twitter is optional. And I choose to answer because I want to and can, I don't need to justify using something for what it was created for as long as I'm not breaking any laws.
My point was you're criticising his choice to reply to her post and then you go and do the same and respond to my comment, it's an observation.
You have every right to criticize what he's doing but it's dumb when you're doing the same thing.