Seeing as a human is higher up the reincarnation chain than an animal, maybe it's because these people feel they've done something they should be punished for in the next life. After all, life for pretty much any animal is nasty, brutish and short. The only blessing is that they're not intelligent enough to wholly realise it. Seriously, I think it's because we can easily see the troubles of human beings: eg David Beckham: fantastic footballer, good looks, loadsmoney BUT hounded by the press and he's married to that ghastly woman; but we imagine the life of an animal to conform to an idyllic preconception eg the noble tiger or the mischievous monkey who we assume is having a lot of fun.
I entirely agree with you: everyone may want to come back as an animal, but then what do they know?