It will not happen. Sorry to disappoint all who had been waiting to go back in time just to see what happens if they kill their great-great-great-great-grandfather.
Actually, even the statement "there will never be any time travel" fails to convey the reality fully. When you talk about time travel, you have to forsake the traditional tenses. Past and future tense can no longer have meaning in a universe with possible time travel. It would be like having different conjugations for walking towards left or walking towards north. Saying "time travel won't happen" is inaccurate, a more accurate statement is "time travel does not happen". Even that does not work: I need a tense to convey past, present and future at the same time, in other words, an omnitemporal tense. (Here is a language with some extraordinary tenses. )
Of course, it is time travel to the past that I am talking about. Time travel into the future is quite possible, and happens at a small scale all the time. But traveling back in time, in Einstein's model of the universe, is the equivalent of going faster than the speed of light, which is basically covering a negative distance. These are both undefined for our universe.
By way of contraction, let's do a thought experiment, and for a second, assume that time travel to past becomes possible in the future. What do we know about human behavior? We know that every single invention has been adopted by various organizations with political or with financial agendas and have been used and misused extensively, and spread until they were available to each and every single being. Therefore, we can easily deduce that time travel will become available eventually to every soul, and will be used for all sorts of different ends. Disagree? Consider for a moment the spread of nuclear warhead technology, arguably the most important military secret of the 20th century. It was first stolen through espionage by Russians. Eventually, different nations started to develop their own models, beginning with countries like France, and eventually becoming available for India, and now possibly moving on towards Iran. We can easily conclude that the same will happen with time travel technology.
When time travel is concerned, it does not matter how much "time" it will take for it to spread. Eventually, when it does, there will be people coming back from the future, and trying in various ways to affect our lives. At some point in every persons lifetime, and at various points in history, we would need to see evidence of future travellers - and not just one, but many. In fact, we would need to see distant stars and galaxies "already colonized." It would be necessary that as early as the start of the human history, even as early as sun's history, many places in and around the solar system would already be colonized.
Paradoxical? The answer is this: For any given universe with sentient, evolving life, time travel either omnitemporally exists, (at all points in time) or doesn't exist at any point. There cannot be a moment in time when it "begins" to exists, because well, it is a time machine, it transcends time. It is omnitemporal if it exists. In other words, if time machine had been possible, we would have been born into a universe where it already existed. Therefore, no time machine, not now, not ever.
Now, can we argue against my statement? First of all, I am assuming Einstein's 4-dimension space-time continuum model, a block universe. As known, this model fails on the subatomic scale, it fails for quantum mechanics. However, for all larger distances, this is the best model we have until now. Of course, with the introduction of quantum physics, we know that some particles actually move back in time. But this does not contradict my argument: If subatomic particles did have an effect, that would mean that we need to observe a time machine right now, because as I argued, a time machine is omnitemporal. But we make no such observation, and thus no time machine does not exist omnitemporally.
However, there are some other models explaining the universe, such as the "multiverse" model, or the "trouser legs" model explained diligently by Dr. Emmett Brown in Back to the Future. Fiction aside, David Deutsch, in Fabric of Reality explains this theory and elaborates on how time travel is actually possible (and even inevitable) in this model. I disagree for the reasons I have explained above.
Therefore, in our universe, on our scale, time travel does not take place. To imply that it might in the future, is a contradiction.