When you die, your body disintegrates, and becomes food for insects, plants and bacteria, and so your body merely transformed into other lifeforms, then reincarnation can be considered literately true. Your consciousness, your mind, your nervous system, will not survive this transformation, but new conciousness, new minds and new nervous systems will form in its place.
If you take it many steps further, you can see how it connects to Carl Sagan's idea: "The cosmos is within us. We are made of star-stuff. We are a way for the universe to know itself.".
Your life, your death is merely one part of the cosmos, transforming into another. One door closes, and many more doors open.