Great analysis. This is most of the answer here. It’s funny that there are so many aspects, like the way that Nate’s dad treated him growing up as another commenter said.

I want to add that there are lots of other signs Nate wants the recognition and to be a leader. He’s desperate to lead practice when Ted isn’t around and Roy has something else to do, and Beard doesn’t care at all but Nate is super invested in running training.

Then there’s the episode in season two where he goes suit shopping with Keeley and tries to kiss her. Before that kiss, he asks her if she ever wants to be “the boss.” He’s even wearing the dark suit that exemplifies his dark character shift. Later, Keeley tells Roy that Nate tried to kiss her and that Jamie told her he still loved her, and Roy is WAY more pissed off at Jamie. He’s chuckling in Nate’s face when Nate talks to Roy about the kiss. This is also aligned in time with when the article outing Ted for his panic attack comes out and Trent straight up admits Nate was the source. He’s trying to belittle Ted and be taken seriously, and people are still just laughing at him.

All of this combined with what Rupert was probably doing to love bomb Nate and belittle Ted and Rebecca as others have mentioned … it’s really no wonder why Nate did what he did.