Enlightened [Elitist] Agnosticism

[One Above All]

The reverse argument would be just as strong: "Technically an atheist is either a gnostic atheist or an agnostic atheist; so if someone says she's an atheist, she's not really saying anything at all."

It wouldn't, actually. An atheist is stating plainly they don't believe. An agnostic is saying they're not sure deities exist. When you're asking someone about whether or not they believe, most of the time, you might actually be trying to find out whether or not they believe.

I'm both an atheist and an agnostic. I choose to self-identify as an atheist, but I don't see any reason to belittle people who self-identify as agnostic.

I do. Plenty of reasons, in fact, one of which is the elitist attitude ("Oh, you're an atheist? So you're sure god doesn't exist? Can you prove it? Now me, I'm an 'agnostic'; I'm much more open minded than you!"), another is the intellectual dishonesty/double standards ("I can't prove there is no god. What's that? You have a dragon in your garage? I don't believe you!"), and then there's the fact that they aren't answering the question that was asked of them. If you asked me about my graphics card, and I said my computer ran Windows 7, would you be satisfied with that answer? Would it even be an answer? You didn't ask the question, so my guess is "no" to both things.
EDIT: Self-proclaimed "agnostics" are like the idiots who, out of options A (theism - they believe) and B (atheism - they don't believe), made up an option C (they don't believe, but they also "don't don't believe"), chose it, and insist it makes sense, even though it's not an option to begin with. Two options: belief or non-belief. You can't have both, but you also can't have neither. Saying you're not sure whether or not the thing you believe or disbelieve exists is meaningless in this context.