While Diana doesn't inherently hate ty-lee, I mean she's just a young adult who grew up with safety from Bruce and then like Diana—she was turned into a Batgirl but unlike Diana, she lived long enough to form her own hero persona meanwhile Diana never got to escape that mantle because she had well died, was brought back to life and then turned into a weapon by the hate she was taught to defend herself with.
So when she sees ty-lee, she sees the version of herself she never got to be and it hurts and sometimes she does wish something would happen to ty-lee.
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