"Yes, and imagine a world with no hypothetical situations"
-Jasper Fforde
Do you believe in free will? Then you cannot travel into the future, even though our understanding of the limits of technological progress almost guarantee that we will have a mechanism for doing so one day.
Everyone knows that going back in time is ridden with paradox: if I return to the year 1955 and kill my grandfather, then I could not have been born, then I could not have made the trip into the past. Contrary to popular belief (and media misperceptions), you cannot change the past. This is not something we would have to worry about, even if we could travel into the past.
However, is time travel into the future really devoid of paradox, as some scientists claim? Suppose Harth, a denizen of Earth in the 23rd century, builds a spaceship capable of approaching 99% of the speed of light, and along with a crew of a few hundred people, he orbits the sun at that velocity for many years. When he returns to earth, he finds that humans have gone extinct, and he sets out to repopulate the planet. Let's say this happens in the year 9001 CE. Now, Jena, a high-society lady of the 22nd century, does precisely the same thing as Harth, and instead travels to 9010 CE where she finds Harth's nascent colony. Remember, Harth has not yet been born. Is he destined to travel into the future?
Just as if I traveled into the past, I would not be able to kill my grandfather if I attempted it (he might cartwheel away just in time), the possibility of travel into the future seems to strip us of our free will. Granted, the paradox is not unique to future travel; it is structurally identical to the problem that arises when traveling into the past. (i) But it is important to recognize from this anecdote that time by its densely ordered nature cannot include paradox in one direction and preclude it in another: the future is the past for a yet later future.
Of course, for travel into the past there is an oft-forwarded hypothesis that claims that I can actually kill my grandfather, and the timeline merely splits at that moment, allowing the reality of my dead grandfather and my non-existent self to fade away into another universe of the multiverse. But for our future scenario, when do the timelines split? Most intuitively, it happens when Jena observes Harth's colony. However, note that this doesn't solve the paradox. If the timeline of Harth's colony splits off of the timeline of Jena's reality at that point (to prevent him from being forced to travel into the future when he is born), does she observe the colony fading before her eyes? This seems implausible...
Since this is a problem that plagues future travel, by extension of (i), it cannot be a solution to the problem of travel into the past. I recognize that this is only a heuristic argument, but I believe it still makes a persuasive case.
There is a logical (although perhaps equally implausible) resolution to this issue. Suppose instead that time-travel itself is the impetus for a timeline split. Then, Harth's body in the future exists in a parallel universe distinct from his body at birth. This solves the Jena paradox and doesn't fix an absolute destiny for Harth. However, if this is the case, remember that by the time dilation inherent in special relativity, even by traveling in a car at 60 mph, you are traveling ever so slightly into the future. You are creating a parallel universe every time you move.
If you find any holes in my logic or points worth exploring in more detail, let me know in the comments: I'd like to keep thinking about this question. Also, if you find the writing confusing, please let me know. I am building slightly complex ideas, and I want the writing to be as lucid as possible so it doesn't impair you, the reader from understanding the concepts I put forth.