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.
Something unusual like extreme stress MAY be causing him to act uncharacteristically, but what bothers me here is that he's not just got fed up and said something rude like "shut up" or "don't be a bitch" or "I'm never going to agree with you on this so no point arguing". He's made a statement about your long-standing relationship and life together that makes no sense to you, and suggests that he sees those things in a very different way than you do. And you had no idea he felt that way. That's serious, and it can't just be ignored, even if he seemingly "goes back to normal" tomorrow.
I'd bring it up at at a time when the two of you have plenty of time and privacy for a face-to-face talk, and are both calm and rested (and sober, if that applies). Remind him of exactly what he said, verify that you heard it correctly, ask him to explain what he means. What has he disliked in the past, what does he intend to do differently now? I'd also ask WHY he has been "pandering" to you (whatever he means by that) and let him know that this is a problem because a healthy relationship is built on honesty and clear communication.
I'd also explore the seeming disconnect in how each of you viewed this argument. From your perspective, each of you has a different opinion about how the dog got hurt, and you have every right to express yours just as he has every right to disagree. "I'm not going to pander to you" suggests at the very least that he thinks you're demanding that he agree with you, or asking him to say something he doesn't believe, or asking for an apology. Does he think that, and if so why? Or does he think it's "pandering" to allow you to express your opinion even though it disagrees with his (which WOULD be a big red flag) - and again, if so, why? Is it "pandering" for you to listen to his different opinion - and if not, why the discrepancy?
Since you asked - if your partner were a woman, I'd say exactly what I said above and would consider the situation just as serious, However, IF there is an element of misogyny in his new "narrative" (and unfortunately, it does have a little bit of that flavor, although there may be other explanations) rather than just a completely egalitarian resentment of you as a specific human being, that's something you definitely want to know about and avoid before going forward with marriage and/or children!!