When you talk to people who believe in reincarnation, it usually turns out that they believe that in their past lives they were Indian Princesses, Medieval Knights, or what-have-you: something fun and romantic. They tend to forget that the odds are very high that they would have been starving tribespeople, workers in coal mines, plague victims, babies who died in infancy, etc. There aren't nearly enough princesses to go around.

My feelings about this are pretty much the same. I wouldn't choose to have been born male to my actual parents; I have only to look at my brother's life to know that wouldn't have been an improvement. If the choice is just to have been born male, with everything else about my life up for grabs --
no way would I want to change. There are around 7.5 billion people alive today, and the vast majority of them lead unfathomably miserable lives: according to a 2013 U.N. study, 2.5 billion people lack access to basic sanitation, i.e. toilets and clean water. These same people tend to go hungry a lot of the time.
So if choosing to have been born male means getting thrown back into the gene pool and taking my chances, the odds I'd have lived a better life than the one I've had, unhappy as it's mostly been, are very small indeed.
I'll take what I've got, thanks -- it could have been a lot worse.