There is at least one situation where I find answering your own question mildly annoying.
If I'm perusing the list of questions, looking for something I can answer, then see a question which I know the answer to, I like to jump on it. Help a fellow out.
Then I'm halfway done writing an answer and the little "Another answer has been posted" banner pops up. I refresh the page to see that the asker has immediately answered his own question, meaning that there was no actual question.
No one wanted to know the answer, because the asker wasn't actually having a problem when he wrote the question. Even if I beat him to his own answer, it wouldn't matter because I wouldn't be helping him, he already knows a working answer.
This situation just wastes my time.
I don't mind answering your own question, but I would like it if one would only post a question if they (at the time) want an answer that they don't have. It's fine to answer your own question later if you discover the answer, be it trial-and-error, research, or a combination of other people's answers.
The difference would be akin to a man asking for the time.
The man asks if anyone has the time. No one answers right away, but someone does mention that it's sometime after 10 o'clock. He realizes that there is a clock on the wall and mentions aloud "Oh, never mind, I see that it is 10:40."
The man asks if anyone has the time. One person speaks up "It's ten fo..." but is interrupted by the first man who, while checking his watch, states "It's 10:40, just in case anyone wanted to know."
For the sake of argument, let's assume that it will always be 10:40 in whatever room this man is in.