it seemed like he was just suddenly selfish and narcissistic
I noted through the series that they make several moments where you see Nate visibly react to what could be interpreted as abandonment, or getting hedged out of a role, overreacting to honest criticism, or being unforgiving of simple mistakes
Nate's dad strikes me as a narcissist in the perfectionist 'you can never do right' way, and Nate as the child of a perfectionist narcissist could end up like a borderline or vulnerable narcissist; when we first meet him, he is very sensitive to criticism and has little self-worth; for him to taste being accepted and then be respected as a coach, then get a little bit of fame
I think we're to understand that Nate is also a narcissist but has never had the position to fully 'bloom' as one until the coaching spotlight inflated his ego