It's hard to be the recipient of downvotes.
At the same time it's a great tool for assessing the quality of posts. It's the same reason HN allows downvotes.
However the dynamic of SO is different. Users are coming to the site to get help and solve problems, not to have open-ended discussions.
SO should have a grace period for new questions. No downvotes during the first 1-2 hours. Aside from being less discouraging for new users it would also mitigate cases of incorrect downvoting. A negative score is a signal to other users that a question is not worth consideration, and dissuades possible answerers from providing a solution.