Since you are french according to your handle, I will direct you to this video, which I liked very much : https://youtu.be/VlWvnhSiuck?si=dvgQQS1Y4oa3A1yO .

In essence, I don't disagree with points 1 and 2. But the conclusions that you draw from these could be used to justify things which, hopefully, you would find morally objectionable. It is not because empathy is not a rational response that we should not try to use rationality to shape our decisions. There are pretty of other feelings/behaviours that we choose to consider bad and worthy of punishment, regardless of the fact they are useful evolutionary tool.

Unfortunately this comment is much too short to make the full argument, but the video I linked does a great job. I was wholly convinced by it, and though I'm not vegetarian, I do try to source my meat from places with more humane conditions.