It is a serious thing that a man should be mourned when he has passed from Man to God by change of state and not by destruction of his nature. Like Valerius, we are all in the process of learning to understand that we are not our bodies, but pure, eternal Spirit focused intensely within the body in order to explore the physical worlds and take responsibility for our individual and collective creations. Now, all this may seem to uphold reincarnation, and though reincarnation is about the best interpretation of reality we can perceive in the space-time continuum of the physical plane, it is nothing more than a good interpretation. In reality, there is no time as we perceive it. Past and future both exist simultaneously with the eternal present.
Reincarnation needs the illusion.
The real danger inherent in the concept of reincarnation is that it is easy to believe in the eastern version of heaven and hell. It is called 'karma'. Punishment or reward in this life as a result of what another of your personalities has done in a 'previous' life. Karma is volitional, that is your choice. To grow in understanding, in love, and in responsibility.