While toying around on SE, I browsed some of my older questions, and out of curiosity, voted to reopen one to see the result. To my surprise my own vote to reopen counts toward reopening. Is this a feature or a bug? If it is a feature why does it exist, as a user would naturally be biased toward their own content, and if it is a bug why hasnt it been patched yet?
This is how it is intended to work. Your own vote does count, and it puts it in the reopen queue for others to review.
As for why it exists: If your question is closed, and you edit it and believe it should be reopened, or if you believe it was erroneously closed, this is the means by which you can express that. Authors of a question have as much of a voice as anybody else. This is a good thing.
I suppose there is "bias" of sorts but in practice it doesn't really make a difference. If the question should clearly be reopened it's going to get reopened regardless of whether your vote counts. If the question clearly shouldn't be reopened then it isn't. And if it's borderline, well, it'll probably end up closed again, and that's OK. Note that users must wait a certain amount of time between casting the same type of vote (close, reopen) on a given question, so a borderline one at least won't go back and forth forever from the same users' votes.
Also remember that reviewers can choose "Leave Closed" in the review queue to counter this. The whole system sort of organically takes care of any bias there.
Note that this comes with the view close votes privilege, which is typically awarded at 250 reputation. The third-to-last paragraph in the Help Center page says, “You may also cast a close or reopen vote on your questions.”