I have read an argument that states that if time is infinite, then we need not worry about death because one day our DNA will return exactly as it was in this life. That is; 1 million ar a trillion years in the future, someone might come into existance with all my DNA (or to go even further into the future,further than we can perhaps imagine, this person may even go through the exact same life experiences I've been through) and this would be a reincarnation of me. Is this even a logical argument? what would make this future person me? I could clone myself now but that doesn't mean that I would experience the internal conciousness of my clone. Similarly, if someone mapped my brain, memories and genome and was somehow able to simulate me on a computer, would this be me?
I'm with you. I don't see any reason to suppose that some future person who happened to share your DNA would be you, no matter how similar the course of their life might be to yours. And that's even before we get to the question whether time in infinite (quite possibly not) and whether, if it is, it has the implications that this argument supposes.