One thing that really makes it impossible is the butterfly effect, Now if somehow we discover a time machine go back in time ,we will then change the very future in which the time machine was invented, this change is gurrantted because of butterfly effect.( for people who dont know what it is watch the movie ,everytime he changed something small in his past his entire life changed : the butterfly effect)
this argument fails if time travel is like tweleve monkeys(i. e self consistent :there is only one time and past,future and present or simply put past depends on future as much as future depends on past . the example provided above then can be explaned in terms that the small change made in past only led to that discovery)
there is only one problem with that - this self consistency can easily be broken. if we record what we said in past and then come from future and dont say the same words that way.(yes there is a argument that universe wont let you change your words i.e that is person from future already knowing he had said some words (he saw the video na) cant change these words but i think he can .how many brackets has it been?
btw that leaves only one possibilty of the creation of new parallel universe i doubt a man made machine can do that
So thats my argument