In a way, Fyodor represents everything Nikolai doesn’t like and yet wishes he could be. Fyodor not only embodies much of his ideals-a man who doesn’t have any attachment to emotion (on the outside at least), but he also has full control of the world around him; that being the thing Nikolai craves to be free. I believe part of the reason Fyodor understood Nikolai so thoroughly was because they share in that need to be in control: for Nikolai it’s of himself, and for Fyodor it’s of his plan, (or the world, it’s purposefully unclear).
Fyodor is not only a serial terrorist (which Nikolai feels awful about being) but he is also The Most controlling character in the series, what Nikolai hates. By killing Fyodor he’s not just getting rid of his feelings for him but he’s also Becoming Fyodor, in the way that then he will finally master his guilt by murdering someone special to him.
Nikolai is very gay by thinking that the biggest emotional attachment he has that he can get rid of to Beat The System is a man who he hasn’t seen since he went to prison forever ago