Disclaimer: This is not my work; everything is written by Tempest Stormwind. I tried to duplicate his original formatting as much as I could.

If someone says something to the extent of any of the following:
  • I am a roleplayer; thus I do not min-max.
  • I purposely make all my characters weak in at least some ways; that makes them better roleplayed.
  • You're dishing out thousands of damage per hit! You're not roleplaying, you're min/maxing!
...And so on and so forth. If those things come up, then they are committing the Stormwind Fallacy: Just because one optimizes his characters mechanically does not mean he cannot also roleplay well. Just because a character plays his character well does not mean he cannot be optimized. As a corrollary, characters who are min/maxed are not automatically played worse than those who are not, and characters who are deliberately handicapped are not automatically played better than those who are not. It's easy to imagine players who are good at either one of those things, or bad at both, or good at both.

Essentially, roleplaying and min/maxing can easily coexist since they are independent of each other.

For instance, in one of my current games, we've got three of the CO board regulars playing along with two others, with a cast of a pair of high-power swordsages, a CHAMELEON (widely held as one of the strongest PrCs ever published), and my Shadowcraft Mage (you know, as in "I can cast any spell from two different schools spontaneously, even if I don't know them"?)... and yet each character is deep enough to cause moral problems, interconnected enough to work as a team, and compelling enough to be an interesting character in their own right. The existence of a single case like this game is more than enough to debunk "Optimizers cannot roleplay" under any scientific or logical reasoning base. Now, it isn't enough to say that it's rare or common, but it is enough to demonstrate existence.

For those of you following logically, you may recognize this: It's the False Dilemma fallacy, actually, just expressed in terms of D&D. False Dilemma is a fallacy that in which one sets up a dichotomy when in truth there is a continuum or independent axes. An common example of a False Dilemma is "You're either for us or against us." It's possible to support neither cause whatsoever and abstain from helping either side, but the statement is set up in such a way to suggest that this is not a choice -- thus it presents you with a false dilemma. Here's a few more "false dilemma" examples, and a proof.

The Stormwind Fallacy is a special case of this applied to roleplaying; a faulty argument in the following fashion:

1. Either you roleplay your character well or you have min/maxed that character.
2. This character is not min/maxed.
3. Therefore he must be roleplayed well.
Conclusion: All good roleplayed characters are not min/maxed, and all min/maxed characters are poorly roleplayed.

The faulty assumption comes at 1 -- I provided an example of one of my games above which demonstrates that you can optimize your characters and roleplay them at the same time. ONE counterexample is all that's needed -- and I KNOW I'm not the only one (I should show you the Real Adventures games the CO boards hold -- several stellar roleplayers there and they're all CO board regulars, in other words min/maxers).
Unless you can either:

1) Demonstrate that this is not a mapping to the False Dilemma Fallacy OR
2) Demonstrate that the False Dilemma Fallacy does not hold,
then the Stormwind Fallacy holds.

For the record, it's named what it is because of an old debate on the DM boards. I (and others) thought that this idea was mind-numbingly obvious, while others thought that it was a logical impossibility. I snapped at one point and decided to formalize it under a handy shorthand name so people could spread it and learn about it a bit more. I was arrogant (still am), and chose my own name.
To this day I still don't think we need it, but since it's commonly cited (and misused), it stays. I do regret naming it after myself, though.