OP the responses you're getting are coming from the best possible place, however much you don't like it. But if you want something less dogmatic...
He then came out with this narrative that from now on he’s not going to pander to me, that he said nothing wrong and that he’s going to be firmer from now on.
You cannot just let this pass, hope he said it because he's stressed and doesn't really mean it. You need to ask him to explain every part of what he said.
What does he mean, not pander? How has he 'pandered' before? What is he going to do differently?
Why did he think that you were responsible for the dog hurting itself? Ask him to be specific. What should you have done differently? If he believes he said nothing wrong, he should be able to answer all of these.
He's going to be firmer from now on. What is that going to look like? Specific examples, not vague waffle.
Then you have to judge what to do based on his answers. But if it sounds like he intends to control your behaviour or opinions, I'm in the leave him camp. If he won't answer your questions or generally discuss it, then that's a serious red flag and again, leave him. He's telling you he's going to be the boss and you're not allowed to have feelings or ideas or opinions, you'll just do what you're told.
DO NOT LET THIS SLIDE.