Whiny players can certainly be a problem. But, it's important to make sure you aren't contributing to that problem. As mentioned above, it's always a good thing to make sure you're not doing something wrong as a DM. And it's just as important to not retaliate against that player, since you'll only be justifying their feelings of persecution.
A year or so ago, I was running a game that had gone much later than I had originally planned. It was about 3 o'clock in the morning and we were just about to begin a major land battle. I was evaluating some mass combat rules for 3E and just wanted to run a straightforward combat without anything bizarre. I told that players that once their army reached the field of battle, I'd give them some time to see the layout and strategize. When they arrived, I showed them the enemy forces arrayed at the other end of the field and told them that I'd give them some time to come up with a quick battle plan before we started.
At that point, my whiny player lamented that they had wanted to scout the field before they arrived there. Nobody had mentioned anything to me about scrying or sending scouts, so I said, "No, you didn't say that to me." The player continued to push, saying that it was unfair that they would have no chance to ambush the enemy. I explained that I wanted to run a straightforward combat and that there really wasn't any need for worry, since I didn't want to overtax my understanding of the mass combat rules. I explained that I had promised to draw out the battlefield on the battlemat so they could see it, and then give them about 30 minutes or so to come up with a plan.
"You're wrong! And everybody here thinks you're wrong! You're not fair," came the reply. It was 3 A.M., I was tired, the game had gone hours longer than I had planned, and the battle hadn't even started, yet. His words rung in my ears. My blood boiled. My fists clenched. One of the other players jumped up and shouted, "Hey, now! *I* never said you're wrong!" A quick glance revealed that nobody else wanted to share the whiny player's "concern" for their well-being.
I quickly formulated 100 different ways for the whiny player's character to die. (1) Cardiac arrest, (2) an unseen red dragon on the field that was only interested in his character, (3) the whole enemy army focusing only on him, ... (100) the Moon falls out of orbit and smashes him to flinders before bouncing harmlessly back up into orbit again. You get the idea.
Then, I sat back down in my chair, pushed back from the table, and took 3 really big breaths. Yeah, that's better. OK. I didn't explain to the players that I really wanted a simple, simple, *simple* mass battle so I could evaluate the new game mechanics. I knew that this was a party that loved to over-plan everything. It was a miscommunication. It was as much my fault as it was theirs. Mister Whinypants -- even though he had completely failed at his Diplomacy check -- was right, in a way. And it really didn't matter that much.
Ultimately, I politely stated that reconnaissance was unnecessary as I wanted something simple. I explained that what they saw was what they got, and there wouldn't be any monkey-business on the part of the enemy force. I explained that I just wanted to test the rules and have some fun. Then I gave them 30 minutes to plan while I took a nap.
That whiny player sometimes makes me want to throttle him. He's trouble. And I often can't stand his complaining. But, in that instance, it wasn't all his fault, and I had to admit that. That PC is still alive, and is doing fine, but we've established that moment in time as a joke within our group: "You're wrong, and everybody thinks you're wrong!"
I've also started a new campaign with a smaller set of players from that original group. The whiny player was not invited to play in this new game, and it's been better because of that. If you can't play without this player, try to see his point of view. Don't necessarily give in to him. Just try to see it as he does. Then, if possible, tell him (out of character, if need be) that when his character whines, complains to, and threatens NPCs, they'll have the same reaction he would if someone whined to him. Remind him that part of being a heroic character is dealing with all kinds of problems, from the BBEG actually stealing the artifact to the ship leaving the dock without all of its passengers.
Ultimately, look forward to the fact that someday, you probably won't have to game with him anymore!
