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The main reason is that space-time is very simple compared to biology, so we understand it much better.

We have excellent reasons to think that we have a very good understanding of space-time, and that understanding -- a simple, elegant, theory that has survived every test generations of clever physicists and astronomers have been able to throw at it -- says "No FTL, no how...or at least not at all easily...it's really, really hard...Nah, don't plan on it."

Biology, OTOH, is complex and we know that we don't know a lot that we'd like to know. While we currently have no way to put someone in suspended animation and then later take them out of it, unaged and unimpaired, we have no theory that says we won't someday be able to do it. All we know is that it's well beyond our current technology.

So if you're trying for the hardest SF which hews as closely as possible to what we know, we cold sleep is a lot more plausible way to get to the stars than an FTL drive.

Cryo sleep is just an engineering problem. We know that water in the cells freeze and burst the cells. That gives us a single problem that we can solve that doesn't force us to rewrite the laws of the known universe. As others have pointed out here, we even have some clues about how to do it since some animals manage to do it.

FTL, on the other hand, requires us to rewrite the known laws of the universe. That is allowed since in our history, every time we've known how the universe worked, we were dead wrong (James Burke, How the Universe Changed). But it is squishier SF since it does require breaking the rules as we currently know them.

Freezing people is likely possible, since nature already does it.
http://www.latimes.com/science/sciencenow/la-sci-sn-alaskan-frozen-frogs-20140723-story.html

We just need to figure out how. FTL so far, we haven't found any examples in the universe where it happens. We almost did, but turned out to be faulty measuring tools.

FTL breaks causality

I haven't seen anyone explain why FTL is impossible. I don't quite understand the nuts and bolts of the proof, but FTL is a time machine. Causality is the notion that "the universe makes sense": that effects never precede the things that cause them, that things cannot cause themselves to happen (or cause themselves to not happen, which is where the trouble really starts). Causality means that paradoxes are impossible, because a paradox requires a circular cause-and-effect circle; one of the links in this chain must cause some effect backwards in time, and causality says you can't do that.

FTL throws causality out the window, because going fast alters the rate at which time flows for you (relativity). This hits an asymptote (infinity) at the speed of light - meaning that going FTL involves crossing that threshhold.

Genres heavily reliant on FTL usually ignore relativity altogether

It's hard for readers to wrap their heads around the idea. It's hard for most writers to wrap their heads around the idea. And it dramatically complicates most space opera.

Battles in which different parts of the battle happen at different speeds are a hard thing to convey sensibly to the audience.

If the protagonists pop over to a neighboring star system, and stay there for a week, it's much more convenient to simply have that take a week. In reality, time would progress slightly differently in each star system (because they have a relative velocity to each other), and going back and forth would be really wonky. Worse, these rates are all related, so if you have five star systems in your story being repeatedly visited, and you wanted to account for time dilation in a way that actually worked, you'd have to actually somewhat understand the math, otherwise people will point out that your dates don't work. (This is the internet, folks ;)

It's much easier to simply slap 'stardates' or 'universal galactic time' measurements on things and be done with it. In most space opera, that's exactly what the writers do. There's nothing wrong with this; action movies don't usually track how much ammunition anybody's using. But it's not hard science.

TL;DR

FTL directly contradicts the current state of the art in astrophysics, and it's commonly used as an enabler for stories that ignore time dilation altogether and have time flow at the same rate everywhere always.

In contrast, cryo-sleep is an excellent choice for hard sci-fi future tech: Given that we know it's possible for some creatures here on earth today, it is quite believable that hundreds or thousands of years of technological development could make it happen.

Cryosleep is already possible, we just don't know how to wake them up again. The general concept of freezing something to preserve it is well-known and it stands to reason that it might be very much possible in the future to wake up frozen humans. That doesn't mean it's certain, but it's very much a realistic extension of our current technology.

FTL isn't an issue of technology. According to our understanding of the most fundamental rules of the universe, mass cannot travel at the speed of light, and nothing can be faster. Now there is always the possibility that our understanding is wrong, but so far, the model seems to hold up and is extremely consistent within itself and with many other observations. If it turned out that things could travel faster than light, everything we know about time, space and relativity is pretty much completely wrong and we have to start at zero. Not to mention the things we do know about time dilation and such would obviously still be true, and it is very hard to imagine how these mechanics would scale to FTL.

Cryosleep provides exactly one thing to a fictional universe: the raw possibility of interstellar travel. But it provides it at a dramatic cost: time. Travelling to even a nearby star system takes years, even if the traveller doesn't experience any time passing. This puts the fictional universe in a position similar to the Age of Discovery, where travel to other continents is possible, but so slow and costly that it is effectively one-way.

FTL, on the other hand, doesn't have this cost. (It may have other costs, depending on the author's choices, but it is -- by definition -- not slow.) FTL travel makes it possible for people to travel back and forth between star systems without time-debt, making casual travel and tourism feasible. It also means that fast communications and trade are possible -- in short, it puts star systems in a position more comparable to modern nations.

What makes cryosleep considered a "harder" SF element than FTL is less the differences in technology than the differences in what they enable. Since cryosleep is much more limited, it is considered less of a compromise.

We're already taking our first baby steps towards "cryo sleep": https://www.space.com/27348-nasa-mars-crew-deep-sleep.html

"Therapeutic torpor has been around in theory since the 1980s and really since 2003 has been a staple for critical care trauma patients in hospitals," aerospace engineer Mark Schaffer, with SpaceWorks Enterprises in Atlanta, said at the International Astronomical Congress in Toronto this week. "Protocols exist in most major medical centers for inducing therapeutic hypothermia on patients to essentially keep them alive until they can get the kind of treatment that they need."

...

Coupled with intravenous feeding, a crew could be put in hibernation for the transit time to Mars, which under the best-case scenario would take 180 days one-way.

...

SpaceWorks' study, which was funded by NASA, shows a five-fold reduction in the amount of pressurized volume need for a hibernating crew and a three-fold reduction in the total amount of mass required, including consumables like food and water.

Overall, putting a crew in stasis cuts the baseline mission requirements from about 400 tons to about 220 tons.

Extending on this to complete stasis that would halt aging is merely an engineering/medical problem. The biggest problem is repairing cell damage from a complete freezing, but "medical nanobots" requires much less handwavium than FTL travel. Therefore, it is "harder" sci-fi.