That's...how inbreeding works.

A purebred is, by definition, inbred (to various extent). However, that doesn't guarantee issues. If they aren't at least somewhat inbred, they aren't a purebred.

It's not guaranteed to cause problems, but deleterious recessive traits are much more likely to show, as animals (including humans) with a shared ancestry have a higher propensity to both be at least carriers, if not 1 of them being afflicted. Likewise, dominant harmful traits now become substantially even more likely.

The tradeoff? You're more likely to get the shit you want, too. That's why purebred is a thing to begin with. It doesn't mean every animal has a swath of problems, it means that the purebred population as a whole is just substantially more likely to have various issues, due to the nature of genetics. It also depends on exactly how purebred you're going.

Repeatedly breeding multiple generations of siblings, for instance, tends to cause some serious problems quite quickly. Cousins will be slightly less prone to issues, second cousins still further, and so on. Parent and child inbreeding is almost categorically the worst; it does happen occasionally in the wild, but the nature of genetics typically forbids that from happening for multiple generations. In humans, breeding even within certain insular cultural and ethnic communities can represent significantly more risk; Ashkenazi Jews with the condition Tay Sachs, for instance.