Speed and perfusion. Big problems both during freezing and thawing:

For freezing, water is the enemy. It expands and forms crystals as it freezes, which together rupture cell membranes and effectively ravage tissues. If you just drop someone into a cryonic vat as-is, the brick of icy cellular mush you get will be far too damaged to ever be viable again. If you're familiar with freezer-burned meat, imagine that happening to everything in your body, including your heart and brain. Not pretty.

The workaround for that is antifreeze. Yes, seriously. Get all the water out of a person that you can and replace it with something that won't crystallize and thaws early enough to allow replacement during resuscitation. But that's where speed and perfusion are nightmares: every minute you're waiting to freeze someone while you replace water is a minute that tissues are dying from anoxia. This is the worst with the brain: it dies really, really fast without oxygen and yet the blood-brain barrier makes it one of the hardest places to achieve non-water perfusion with.

That said, there have been advancements with this where cooling the body to just about freezing to slow neuronal cellular death combined with better antifreezes and techniques might get us close to reaching "frozen" with something that's still viable. A rabbit brain was successfully frozen and thawed using some of these -- though, notably, not yet in a rabbit: https://www.newscientist.com/article/2077140-mammal-brain-frozen-and-thawed-out-perfectly-for-first-time/

So we might be kinda-sorta close to getting cryonically frozen humans that are damaged lightly enough bring back. Very doubtful anyone frozen today is, but we might be there within a few decades.

Thawing is even harder, though. Even in the best-case scenario, you have a bunch of critically oxygen-starved tissue frozen; every second of anoxia counts once things unfreeze, and the brain in particular really needs to go from frozen to "warm and oxygen-perfused" very, very quickly. Human brains are really dense and, as mentioned, really hard to permeate -- we don't currently have much of any clue about how we'd warm a brain out of cryonic suspension enough to restore blood and oxygen without having orders of magnitude more anoxic duration than those brains can take. Exotic ideas abound about blood replacements that can achieve oxygen transport while still perfusing a very cold brain, but it's all total conjecture at this point.

And that aside, the dance when you restart everything else in the body is hard, too. You need to swap all of the liquid in the entirety of very complex human vasculature -- including at least most of what exists intercellular media and the like -- and restore circulation with oxygen very, very quickly and very, very consistently. Simplifying a bit, but if you hand reaches 1C while your arm is still -2C, you're going to have a bunch of things in your hand die while your arm is waiting.

We don't have any real line of sight on how to achieve this super-fast, super-consistent, super-precise reoxygenation of a big, complex organism with all of the systemic coordination that's necessary. There's nothing to say it shouldn't be achievable someday, but let's just say we have no reason to believe it'll come sooner than commercial fusion.

But why are embryos OK? Because they're small and easy to perfuse! You can get all of the damaging water out of embryonic structures and flash freeze it way before the lighter anoxic time constraints kick in, and it's not (comparatively) hard to warm and reoxygenate them quickly and consistently enough to have them in a good, healthy state years and years later. Smaller organisms -- especially ones that evolved resilient structures -- can already be revived that way, too: tardigrades and other similar animals have been thawed after tens of thousands of years: https://www.smithsonianmag.com/smart-news/scientists-revive-tiny-animals-spent-24000-years-ice-180977928/