Let's go through the logic first. The following statements are suppositions that must be chronologically accepted.
- Matter is neither created nor destroyed.
- Matter is made up of atoms.
- I am made up of atoms.
- I am matter.
- Therefore, I cannot be created nor destroyed.
Now here's the philosophical (or perhaps, ideological) part:
With respect to statements 3-5 above, what defines "I"? Am (or Is) "I" the atoms that compose my form or am (or is) "I" the identity that I have created for myself?
If "I" am my atoms, then when "I" die, I will continue to exist because my atoms will, albeit in a different form - a different incarnation hence, reincarnation. If "I" am my identity, then when "I" die, I will cease to exist.
I think the former highlights a type of belief common in eastern philosophy (we are the universe) whereas the latter is common is western philosophy (We live in the universe, or we observe the universe).
Perhaps one's identity is linked with their atomic structure (i.e., the chemical processes of the brain)?
Do you think my reasoning is sound?
Edit: to make it clear, I am supporting the idea that if one believes that "I" is based on the existence of atoms, then reincarnation is in fact real.