He "hates" his ex but she is still in his life

We've been dating for about a year. He's told me that his ex cheated on him and he hates her guts. They broke up I believe a couple years ago. I wasn't snooping through his stuff, I never do because i trust him. But he posted a pic on his IG and she liked it. So I checked out her page and not only does he follow her, but he also likes her pics. I confronted him about it and he got defensive and said he liked her pics to "be petty." This is not normally something I'd care about but the fact that he claims to hate her and then gets defensive and won't unfollow her makes me uncomfortable. He's given me no reason to mistrust him so idk if I should just let it go and not worry about it or insist that she be eliminated from his life. I love him very much and would hate to end things over this, but if he has feelings for her still he should not be dating me. Any advice would be greatly appreciated