This is an important part of Dungeons & Dragons 3.5, and by extension, Pathfinder, history and community, and this site should include a copy of it.
The fallacy, in short, is that optimizing prevents roleplaying, or that roleplaying prevents optimization. It is called the Stormwind Fallacy after Tempest Stormwind, the WotC forum poster who first wrote up a thread dealing with the fallacy and indicating its fallaciousness.
The fallacy is often indicated when any claim of contention between roleplaying and optimization is made, but Stormwind himself does not go that far. Instead, the claim is only that the two are not mutually exclusive, that "one must not optimize in order to roleplay" is a fallacy.
Further, while it's in reference to D&D 3.5 (and uses system-specific references in a few cases), the larger concept is applicable to almost any roleplaying system.
Without further ado, the original formulation by Tempest Stormwind on Wizard of the Coast’s forums, including his quotation of another poster that committed the fallacy.
I still stand by the argument that this is a fundamental difference between old school (basic D&D: 1 race/class, AD&D: very limted multi-classing) vrs new school (I buy a book and there is a class in their and I want it gimmie gimmie). The trend I see is old school = roleplayers, new school = optomizers.
Note to New school people: Don't listen to what you hear, you aren't a dork if you roleplay. It is ok to indulge in what D&D is all about, roleplay. If you try it and have a good DM, I guarantee you'll have a blast and won't care so much about optomizing.
Okay, that's it.
I'm hereby proposing a new logical fallacy. It's not a new idea, but maybe with a catchy name (like the Oberoni Fallacy) it will catch on.
The Stormwind Fallacy, aka the Roleplayer vs Rollplayer Fallacy
Just because one optimizes his characters mechanically does not mean that they cannot also roleplay, and vice versa.
Corollary: Doing one in a game does not preclude, nor infringe upon, the ability to do the other in the same game.
Generalization 1: One is not automatically a worse roleplayer if he optimizes, and vice versa.
Generalization 2: A non-optimized character is not automatically roleplayed better than an optimized one, and vice versa.
(I admit that there are some diehards on both sides -- the RP fanatics who refuse to optimize as if strong characters were the mark of the Devil and the min/max munchkins who couldn't RP their way out of a paper bag without setting it on fire -- though I see these as extreme examples. The vast majority of people are in between, and thus the generalizations hold. The key word is 'automatically')
Proof: These two elements rely on different aspects of a player's gameplay. Optimization factors in to how well one understands the rules and handles synergies to produce a very effective end result. Roleplaying deals with how well a player can act in character and behave as if he was someone else.
A person can act while understanding the rules, and can build something powerful while still handling an effective character. There is nothing in the game -- mechanical or otherwise -- restricting one if you participate in the other.
Claiming that an optimizer cannot roleplay (or is participating in a playstyle that isn't supportive of roleplaying) because he is an optimizer, or vice versa, is committing the Stormwind Fallacy.
How does this impact "builds"? Simple.
In one extreme (say, Pun-Pun), they are thought experiments. Optimization tests that are not intended to see actual gameplay. Because they do not see gameplay, they do not commit the fallacy.
In the other extreme, you get the drama queens. They could care less about the rules, and are, essentially, playing free-form RP. Because the game is not necessary to this particular character, it doesn't fall into the fallacy.
By playing D&D, you opt in to an agreement of sorts -- the rules describe the world you live in, including yourself. To get the most out of those rules, in the same way you would get the most out of yourself, you must optimize in some respect (and don't look at me funny; you do it already, you just don't like to admit it. You don't need multiclassing or splatbooks to optimize). However, because it is a role-playing game, you also agree to play a role. This is dependent completely on you, and is independent of the rules.
And no, this isn't dependent on edition, or even what roleplaying game you're doing. If you are playing a roleplaying game with any form of rules or regulation, this fallacy can apply. The only difference is the nature of the optimization (based on the rules of that game; Tri-Stat optimizes differently than d20) or the flavor of the roleplay (based on the setting; Exalted feels different from Cthulu).
Conclusion: D&D, like it or not, has elements of both optimization AND roleplay in it. Any game that involves rules has optimization, and any role-playing game has roleplay. These are inherent to the game.
They go hand-in-hand in this sort of game. Deal with it. And in the name of all that is good and holy, stop committing the Stormwind Fallacy in the meantime.