"The same reasons anyone likes or dislikes a character. Kate died because the actress playing her wished to leave the series, otherwise she might still be in the series, who knows.
But getting back to your question not everyone likes all the characters, in the same way we don't like everybody we meet or work or study with, it's just a fact of life. You can't please everybody all of the time"

"Ziva has changed from her past ways of doing things. She still can kick butt if she has to, but we have seen a kinder, softer side to her as well. A side she most likely never knew was there. I don't compare Ziva taking Kates place because they are too totally different people. I liked Kate, but Ziva is a better stronger minded person to take on a tough job. Kate was more girlie, femenine and weaker in body. Ziva got her killer, her own brother, so you could say she saved Gibbs life and got revenge for Kate as well. Gibbs trusts her now, so I don't really see there is any problem with her about the trust issue anymore. Her 'ninja Barbie' ways are part of what she learnt with Mossad. Its a type of karate moves that she does. People who are taught self defence could do some of her moves. I don't see that any character was written down to make her look better. They all have their faults. Tony is the only one whom the writers let down where his character is concerned, and it has little to do with Ziva. "

"If others like yourself can do her moves then her character can't be so unbelievable.

I don't have anything against Ziva. "

"I find her deeply unpleasant.
She cannot control her temper and lashes out like a spoilt child when she gets cross.
She takes no reponsibility for her own decisions and blames those around her when things go wrong.
She shows no respect for her collegues but demands their respect
She does not learn from her mistakes and no one expects her too.
She has so many talents she is virtually an entire agency in her own right
She is Hollywood's answer to a strong woman. Kick ass and sexy but incapable of logical thought or action when her emotions or hormones are rampant."

"I thought I had elaborated on why I find her unpleasant. I don't like violent, uncontrolled people. And Ziva has not got more emotional in my opinion. She was already that way from the start. Ziva has been ruled by her emotions since the day she first arrived. That is probably my point. She defied logic to protect Ari, flew into a rage when Rivkin's motives were challenged and then did the exact same thing over her mentor. This is not evolution. Its someone who appears incapable of learning from her mistakes.

And please don't tell me what to do. It is offensive."

"
P.S. I am not tring to tell you what to do. I am just saying that when you come back mean it is equivalent to you yelling at me. I really didnt mean for it to be offensive."