Example of another scenario:
The Paladin PC (played by player in question) wanted to utilize
So he readied the action to "use Valorous Smite when all enemies move" so that he could gain the "Hit" benefit of above power against every enemy in range, assuming they were going to surround him. There was no specific enemy or square chosen for the readied action - the player argues that he doesn't need one.
If an enemy (any enemy) happened to end it's move near him than he could use the readied action as an immediate reaction to the movement. But there is no target to his trigger, its just an ambiguous enemy. All he needs to do is pick an enemy and he's good, but he doesn't want to in case that enemy doesn't move next to him. I mean why doesn't he just move into a position, instead of readying an action and just use his power? Or just pick an enemy instead of a trigger with no target? What if another enemy, other than the group of enemies he was talking about moved near him? By his logic he should be able to attack any enemy as long as they move near him - which seems fine but does not seem to jive with the ready an action rules that discuss having a target. Unless he targets a square in front of him, which I suggested...."if any enemy enters this square I attack them" seems to be alright with me. Now I could be totally not following the ready an action rules but I have read them and done a little research and I think you have to have a target...then again I could be wrong, not the first time - definitely not the last.
I'm actually with you in this scenario. When I was suggesting that maybe you might need to be more flexible, it was really in regards to the first example which there did not seem to be any apparent benefit for his request. However, in this case he clearly just doesn't want to follow the rules.
By the rules, it specifically does say you choose a specific action, and an intended target, and a specific trigger. He can't simply say, "I want to attack a monster at my convenience with this attack once I'm happy with the way they become positioned." That's not specific at all.
Personally, I might allow a *little* bit of freedom as far as the target, but if I do, I'm going to require a more specific trigger. For example, I'd probably allow, "the first monster that moves adjacent to me", or maybe even "once 3 of them move within 3 squares of me" or even "the first one to cross this line".
However, I wouldn't just allow them to hold an action until they saw an opportunity that looked good. That's not the intent of the rules, and that seems to be clearly abusing the intent of the rule.
Be firm with him. If he asks for something clearly against the rules and you don't feel there is a good reason to bend the rule, stop him. Be direct, "I'm sorry but that's not a legal move." If he objects, and you are sure you are right on the rules, maybe say, "the rule is quite clear on this one, I think the rule is reasonable, and it's not one that I'm interested in house-ruling at this time." If he objects further, respond with something like, "I think this is the right call. In the interest in keeping the game moving, let's discuss this further another time. Please, let's continue."
However, I do want to point out, in case it's not obvious, if you do convince him to be more specific with his targets, don't use your DM knowledge to thwart his readied action. If his readied action is in response to a reasonable prediction of what the enemy will do, don't deny him that. Let him benefit from them enough that he doesn't feel like he's being cheated.