The only reason not to free Bellatrix Black should be the danger of her attacking other people later on, and that's the point on which he should seek reassurance from Quirrel (re: what they are going to do with her once freed).
Another reason is that (as pointed out elsewhere) there could be other people much more deserving of being freed; freeing Bellatrix or freeing her first might cost him the opportunity of freeing any of them in the near future.
And failing to free her at all may cost him the opportunity to save the world. Harry should have had some doubts as to whether he was ready for the mission.
Failing that, the other thing that has been bothering me for a while is why did Quirrel take Harry to save Bellatrix now? If Quirrel was pure Voldy he wouldn't care about Bellatrix, he doesn't love her. Saving her now, by taking a young idealistic boy on an important high-stress mission, doesn't seem like a good plan. How much does an evil overlord value saving henchwomen, what risk is worth it?
I am not...
[Update: and now there's a fifth discussion thread, which you should probably use in preference to this one. Later update: and a sixth -- in the discussion section, which is where these threads are living for now on. Also: tag for HP threads in the main section, and tag for HP threads in the discussion section.]
The third discussion thread is above 500 comments now, just like the others, so it's time for a new one. Predecessors: one, two, three. For anyone who's been on Mars and doesn't know what this is about: it's Eliezer's remarkable Harry Potter fanfic.
Spoiler warning and helpful suggestion (copied from those in the earlier threads):
Spoiler Warning: this thread contains unrot13'd spoilers for Harry Potter and the Methods of Rationality up to the current chapter and for the original Harry Potter series. Please continue to use rot13 for spoilers to other works of fiction, or if you have insider knowledge of future chapters of Harry Potter and the Methods of Rationality.
A suggestion: mention at the top of your comment which chapter you're commenting on, or what chapter you're up to, so that people can understand the context of your comment even after more chapters have been posted. This can also help people avoid reading spoilers for a new chapter before they realize that there is a new chapter.