The phrase 'my first' refers back the drinks. 'I'm still on my first' means 'I'm still drinking my first beer' (of the evening). The assumption is that the more drunk you are, the more emotional you feel. It also goes without saying that men only say that they love their friends when they are drunk (and then probably regret it later). Joey is drunk, so he says that he loves Ross. Chandler has had less beer than Joey, so he hasn't yet got to the stage where he's drunk enough to say this.

He's still on (still drinking) his first beer. Alcohol lowers inhibition. Chandler hasn't drunk enough alcohol for him to tell Ross he loves him. Of course Chandler is an enormously sarcastic person and never misses an opportunity to make a quip or comment like this.

"I'm still on my first beer." So he's not drunk enough to say "I love you." :)