Next time you think Batman is a jerk, remember this scene.
He might have an aloof manner and come across as cold or even rude, but deep down he is a unselfish, caring man. Why else would he risk his life night after night to save a city who doesn’t even know his identity? He has to put up a shield in order to deal with the atrocities he sees every night that he puts on the cowl and to distance himself from his Bruce Wayne counterpart. Any “softness” would be perceived as a weakness, and his enemies would be quick to exploit it (Joker has taunted him for his “no kill” rule many, many times).
When she was a small child, Ace accidentally used her telekinetic powers on her parents and sent them into a catatonic state. Afterwards, she was sent to a government training facility so that her powers could be studied. She remained there until Joker abducted her and attempted to harness her powers for his own nefarious purposes. For most of her life, Ace was used and manipulated by others, and as she was dying she had no one to turn to.
But Batman was there. He held her hand and stayed with her until she died, providing her with comfort for the first time in years. He knows what loneliness feels like, and he didn’t want this girl to spend her final hours alone and frightened. And so he sat next to her on the swing, held her hand, and comforted her.
A callous, abrasive jerk wouldn’t do that. But Batman would.