My headcanon is that back in the day when Nico was with Jenson, he caught Lewis hooking up with Seb at a club (Lewis could not get the blond German that he wanted, so he went for the one that was available and Seb was just in for the ride). Nico is left fuming and that's when Jenson realizes their relationship has expired.
And even after Lewis and Nico are together, he still gets annoyed by Seb and takes a LONG time to get over that. So, when Nico eventually meet George Russell years later, he's just TRIGGERED because Georgie unfortunately has a Sebastian-esque je ne sais quoi about him.
So, Nico's instincts go a bit berserk. Plus when Max and George are shook by the mention of George, Nico decides to take matters into his own hands and have a little talk with Lewis' high-functioning PA.
Nico was soooo pissed when he saw Lewis making out with Seb; like why would he do that?? Why would he?! He just can't get the real thing so he'll take second best?? (Meanwhile Jenson is Realizing Things in the background)
Nico is just overall a jealous person; only of people he deems worthy of his jealousy, but when that happens... it's tough.
And George just has this vibe around him, and different to other co-workers or assistants of Lewis', George (as a personal assistant) is very personally involved with Lewis and his affairs, and Nico feels like this encroaches into his realm of Lewis' life.
So naturally Nico hates him a little bit.