Fixed mindset. The sentence shows a fixed mindset because the person speaking has a locked in position and isn't willing to chance their mind. A person with a fixed mindset isn't going to want to change their opinion, and focuses on the negative. If this person had a growth mindset, they would be looking for some common ground they both have, and would acklowlage that while they have lots of different likes, they have at least SOME middle ground.
