bouncing off of something @wrldwrn said - and this is not /MY PERSONAL/ take on eggsy, it’s what i believe charlie thought - i genuinely think charlie did not take eggsy seriously as a candidate, not in the beginning. it wasn’t just jabs and jokes, he didn’t just tease eggsy about it (though he did). i firmly believe it did not hit him fully until the parachute test that eggsy actually could potentially beat him in training. i think that was genuinely the moment for charlie where he realized eggsy is braver than he is, came up with the solution much quicker than charlie and had the balls to follow through. up until that point? eggsy is there, sure, and charlie fckn LOVES teasing him ... but he doesn’t take him serious at all as a candidate.
roxy, on the other hand? regardless whether i work of the headcanon that they knew each other fairly well before training or not, roxy is genuinely “threatening” to charlie in a way. i think he’s a better judge of character than he shows - his own included. he knows he’s a dick and he’s not ashamed of it - and i think it’s safe to say he both acknowledges that roxy is determined and smart and capable of kicking his ass and is aware that she, out of anyone, is the one most likely to beat him. important here? and i think that’s pretty much movie canon as well? he RESPECTS her in the most genuine way that he can respect people (again, he’s still a dick!) he is a little shit to her but to some extend he listens to her, can work WITH her (as seen in the first test). it’s a genuine rivalry and charlie can work with that, enjoys that actually cause it pushes him to do better.
(also again, i have a long not fully written out headcanon about the parachute test and charlie taking roxy’s place in jumping first - making a comment about it. i genuinely think there’s less animosity there than he’d like to make people think...)