“Stability” is probably the most mis-used word in the Linux world.
It means that how your system looks and behaves doesn’t change, which is really important for servers, especially in business, where you want to plan any change in advance before you commit to it.
Arch is not stable in this sense. It constantly changes, and those changes can come up on short notice with any upgrade.
But when people read that Arch isn’t stable, they think the system can break at any time.
I’d say this hasn’t been the case for at least 10 years now. If you RTFN (read the fucking news) and use the AUR sensibly, Arch has become a really boring system, regarding breakage.