Occasionally I will pop over to the Trading Post to breed my male squirrels with females -- and more often than not the females that appear when I set my preferences are either alpha females or have been bred already this season.

It's really annoying because sometimes they're being bred for free but lo and behold... I can't breed them because they're an alpha.

It's a really weird issue, I'm not even sure if it's a bug or just something that was never really looked at.

It's not really a bug

What happens is they put their female up for breeding, then while the female is still for public breeding, she becomes alpha. This makes her still technically up for breeding, but unable to he bred to (due to being alpha)

This. Also, I don't believe there is a way to prevent alphas from popping up in trading post, but to prevent squirrels that have already been bred from showing up you can check the box next to "Unbred" in trading post. Doing this may at least get rid of a few non-breedable squirrels from the search :)

There's a suggestion to remove alphas from public breeding:

https://wolfplaygame.com/forums.php?f=22&t=6512