The main issue with freezing is ice crystals forming that puncture the cell membrane and uneven freezing leaving some parts still functional, but unable to function because other parts they need to function are already frozen.
At small enough sizes (about mouse size) we can freeze things rapidly enough that the ice crystals are really small, so they won’t puncture the cell, and the frozen gradient is also really small, basically the whole things freezes and thaws at the same time.
Then, it turns out, being frozen doesn’t actually affect the ability of a cell to function as long as you avoid those two issues.
In conjunction with the ice crystal component described by u/Quaytsar, what’s important is how the sperm is frozen. Sperm is typically frozen at very low temperatures (-200C or so) with the help of what’s referred to as [extenders](https://en.wikipedia.org/wiki/Semen_extender) – chemicals like glycerol or ethylene glycol (common in antifreeze) that help minimize or modify ice crystal formation so the sperm cells aren’t damaged.
Also important – many cells *are* damaged and *don’t* function after freezing and thawing, but the sheer numbers of frozen sperm in a sample mean that you can lose 90% of the sperm and still have a successful fertilization.
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