Jasper is seen as abusive because they are BOTH abusive towards each other. Garnet states it plain. "THEY are really bad for EACHOTHER."

Notice that it's not "Lapis is really bad for Jasper" or vice versa. It's that they are both terrible to each other, but the thing most people focus too heavily on is Malachite.

Before Malachite is where we REALLY see the grounds for Lapis's hatred of Jasper begin to form. She gets snatched up by her and Peridot, interogated and manhandled and physically intimidated. Lapis is their 'informant', and as far as they know, on Homeworld's side. And yet she's thrown into a cell and dragged around by Jasper.

After the ship crashes, Lapis immediately tries to fly away to escape the situation. Jasper grabs her out of the sky, holds her still and coerces her into fusing with her (notice her language being used, it's incredibly manipulative). Lapis accepts the fusion to get revenge, take out her anger and rescue Steven. Only one of those things was a good reason, and even then it was unnecessary (but not in Lapis's view, because she has no idea that Garnet could beat Jasper in a one on one fight).

Then comes Malachite itself, which shows Jasper and Malachite struggling to get control of Malachite. This scene is what paints Lapis out to be abusive right from the start - she's clearly seen wrestling with Jasper for control or dominance in their fusion (representing their relationship) and when she has it, Jasper is shown to be struggling underwater.

But a key thing to note is that when LAPIS goes underwater, when she resurfaces, she ALSO is shown to be beaten up and gasping. This is what confirms that they're both wrestling for dominance or control in the fusion, and as such, abusing each other.

I'm honestly beginning to question where you guys see all of these 'Lapis abused, Jasper abuser that's it' posts because I see far more of the opposite overall...