I remember when the Honor system was first rolled out you could give Honor to ANYONE, ally or enemy - and I think you were also able to Honor multiple people (correct me if I'm wrong). While under the new system you can choose _why_ you're giving the Honor - which is a nice touch and lets them know what they're doing right - I honestly think the old system was better.
1. I liked being able to give an enemy player an Honorable Opponent, as it reminds players that skilled and honorable opposition is part of what makes the game fun. Obviously I can just TELL an enemy player that I think they played well, but I'd like some way for that to be officially included in the game too so other players can see when someone has a history of being gracious to BOTH teams, not just their own.
2. The way it is now feels very restrictive, with the Honor screen popping up after the game more or less screaming in your face 'HEY HONOR SOMEONE' - but you only get to do one. First of all, I only like to give Honor when I feel that someone has excelled, not every game just because - and secondly, what if TWO of my allies went above and beyond, or one ally and one enemy are both deserving of Honor? As I said, it feels restrictive, needlessly so.
I know people will probably think I'm a nerd for saying this, but I genuinely like the Honor system as I feel it's more important to reward people for their successes than to punish them for their mistakes. I think it's a shame that more work hasn't been put into refining Honor and I hope that Riot rectifies this at some point in the near future.