I also hate the question "what do you do?"
Though I've figured out a couple things about it that have be helpful.
First, I realized that most people don't know what a software engineer is, so they are left tongue-tied. Which is easy to misinterpret for rudeness or indifference - but it's usually not. So those "hard looks of negative judgment" could just be hard looks of "I don't know what to say so I won't sound dumb."
Either way I have developed two strategies that usually work to smooth this moment over.
One is to say "I make iPhone apps" (even though I do other things, too). People generally know what that is, are impressed, and say "cool!" and then the conversation can easily move on to other topics ("What do YOU do?" usually lol)
Alternatively I front-load with what my company does. "I work for a company that does smart lighting. I do the software part of it" usually means something to people and they'll respond with whatever they know/have thought about smart lighting ("oh like product x?" "Your company should make a product that does Y") which is, at least, a conversation.
