I don't think Jayfeather has been that bad, and I most certainly don't think he's abusive. I honestly think that word is being thrown around way too much in this fandom. Harsh, yes, but not abusive.
That being said however, I can sort of see where Jayfeather is coming from: Alderheart, his apprentice and the one who will succeed him, was spending a lot of time being concerned over Twigpaw instead of doing his job, or at least that's how Jayfeather saw it. And he wasn't entirely wrong, either, especially since Alderheart has shown to get distracted before. He also saw as Twigpaw getting in the way and, again, he wasn't entirely wrong on that either.
There's also the fact that Jayfeather may be a little jealous of Alderheart for being Bramblestar and Squirrelflight's biological son, as well as trying to push him to be the best medicine cat he can be. After all, it has been shown that despite everything, Jayfeather is proud of Alderheart.
Also, just because someone
looks fine on the outside, doesn't mean they
are on the inside. Jayfeather doesn't even appear all that much in either
Dovewing's Silence or
Bramblestar's Storm, so for all we know, he could've been upset about it all this time and we just didn't even know it. Jayfeather isn't exactly the type of cat to let his true feelings out anyway. Lionblaze and Dovewing didn't get used to the loss of their powers for a long time, so who says the same thing can't be said for Jayfeather?
The life of a medicine cat is also a very lonely one, and this is especially true for Jayfeather. He's blind and was forced to become a medicine cat, he lost his powers and doesn't seem to have as strong of a connection to StarClan as he used to, he doesn't seem to be close to Leafpool even before he knew she was his mother, many of his Clanmates died in just a few moons alone, including his grandfather and sister in the Great Battle, he doesn't seem to be very close to Bramblestar and Squirrelflight nowadays, he isn't all that close to Alderheart and Sparkpelt, his brother has a family of his own, his real father is in a different Clan and his half-brother hates him, and the only cat he's ever loved has been long dead for years.
And then there's this quote from
Thunder and Shadow:
Jayfeather has also shown kindness regarding Twigpaw.
Then there's his age to take into account. Jayfeather's referred to himself as old, and while he may not be that old compared to other cats, stress is a cause of aging faster.
Jayfeather isn't abusive at all. If anything, I see it more as tough love.