The idea of time travel is a nice subject in science fiction but science makes little effort to rule this out. When Gödel obtained time like closed worldlines from general relativity, he thought that he proved time to be an illusion rather than a real thing.The results however have been taken as a real possibility.
I think that people need some mystery, therefore they do not make enough effort to refute this claim beyond reasonable doubt.
Common logic is not highly regarded as a credible tool.