When Ziva just came for the first time, why did Abby dislike her so much? Is it because of Kate's death?

Personally I think there were a number of reasons why Abby disliked Ziva so much at first.

One, Ari was Ziva's brother, Ari killed Kate. Kate was a pretty close friend of Abby's, so this would have made it hard for her to like Ziva.

Two, it would have felt like Ziva was replacing Kate. Ziva got her job, her escrivaninha, mesa etc.

Three, Abby was still grieving for Kate and she would have considered Ziva to be apart of that. So she projected her grieve into anger towards Ziva.

I think alot of her "dislike" came from her grieving for Kate. It's always hard when you lose someone but the ncis team is like family to each other, so when Kate died & Ziva stepped in I'm sure Abby felt like she was trying to take Kate's place.

I don't think Abby diliked Ziva, I think she was depressed because Kate had just died and felt like Ziva was trying to take Kate's place.

Because Ziva was a new memeber at that moment.

she thought that Mcgee liked Ziva.