Edit: for those downvoting, the article linked is actually a pretty good introduction on why time travel may be self evidently impossible through simple logic (we already know the event didn't happen, so it can't go back and happen), but also may be self-evidently possible if certain criteria is met first (specific fuckery involving time-like closed loops and multiverse theory, which means, essentially, history can't be trusted or multiple concurrent histories can't be trusted, respectively).

So, yes, it is confusing to need to think about logic in the terms presented by the article.