Is it a possibility? Sure, I think it's possible. But it's also possible that all this is a dream and when I die, I'll wake up from it. Whether or not you believe it to be real or fake is up to the individual.
Hindus & Buddhists see reincarnation as something undesirable, not a second chance. Their goal is to break free from the nasty cycle of rebirth by attaining enlightenment. Not that I give a crap since I don't buy into their worldview.
Exactly. Whether you believe in reincarnation or not, having to go through another round of mortality is supposed to be undesirable. Birth, sickness and disease, old age, death, Buddhists call these the 4-fold miseries and they are inescapable conditions for all levels of rebirth.
According to Buddhist beliefs, while human existence is thought to be higher up on the rebirth ladder- freeing oneself from suffering by escaping rebirth, especially into one of the 'lower realms' perceived as having worse suffering such as an animal existence, is seen as the highest achievement along with also freeing other sentient beings from suffering.
*An interesting little tidbit- Apparently in animal existence the pressure is off when it comes to generating wholesome karma for a higher rebirth, as the being reincarnated as an animal 'works off' it's accumulated unwholesome karma simply by being forced to exist with the limitations of being an animal.