The Joker should not be humanized. If you give the Joker a girlfriend, what does that tell people? He can carry on relationships with people, just like anyone else. Additionally, it gives him someone to talk to, to bounce ideas off of, to explain things to, and to just generally have conversations with. More normal activities.
Joker isn't, and shouldn't be, normal. To relate to Joker is to fear him less. To fear him less is to respect Batman less. To respect Batman less is to fear Joker less. Before you know it, we find ourselves once again in the sixties.
Joker is scary, and shouldn't have a girlfriend. He should talk to himself, he should be unable and unwilling to have working relationships with other people. We should be entirely unable to relate to Joker.
One time, Marvel and DC had a huge, tag-team, cross-over bash. Superman hung out with Captain America, all kinds of stuff like that. In this cross-over, Joker knew something was amok. No one else did.
One time, Batman was unconscious at Joker's feet, and Joker could have unmasked him and discovered who he was. But Joker said, no, I shan't. If I do, what purpose will I have?
We should not understand Joker.
Therefore, I don't like Harley Quinn.