You're both right that it's more about mental stuff than emotions. I was confused about this same thing a while back and found this really helpful guide at https://spiritualteacup.com/d/264-the-ace-of-swords-as-feelings about ace of swords as feelings that explains it really well. It talks about how the card represents fresh perspective and breakthrough moments in how someone thinks about you. So it might mean they're seeing you in a completely new way or having some kind of realization about the situation. It's actually a pretty positive card to get even though it doesn't show traditional warm feelings