One thing that is common to many people, regardless of their beliefs, is that when someone dies we somehow feel that the person is not completely gone from us, we feel there is still something alive and present. Mostly, we cannot bear the thought that we are forever separated. That brings too much suffering. No matter what our background or culture is, this feeling is universal.
In this world, people are continuously discovering new things. Some things which were earlier thought to be impossible, turn out to be possible later on. It seems to me that the case of life after death is also like that. One can have doubts, but one cannot exclude the possibility that reincarnation exists.
There are lots of people who remember, or think that they remember, their past lives. This is not something only happening in Buddhist countries or among people who believe in life after death. It is something that people can not totally explain. Therefore, reincarnation should be something which at least has to be categorised under doubt.