I'll start off by saying, I am favor of a debate, or a series of debates, between the candidates for prime minister, and separately between representatives of the various parties for Knesset. I think the issues should be laid out clearly in a way that the public can easily understand the various positions and be able to make an informed choice.

That being said:
I understand why Bibi is hesitant to debate Yitzchak Herzog (he says he is considering the matter). Bibi is the sitting Prime Minister, more or less running on his record, basically ahead in the polls, with everything to lose in a debate.
I understand why Herzog wants a debate. His campaign has been lagging. He seems to be behind, and  slowly falling further behind. Herzog has nothing to lose in a debate.

What I don't understand is why they are so reluctant to include Livni in the debate.

One of the conditions stipulated by Netanyahu is that the debate be between himself, Herzog and Livni.

Personally, I think it is a reasonable demand. Hamachane Hatzioni has presented and campaigned on the rotation agreement saying they will serve equally as prime minister, so she is as much a candidate as Herzog is, even though she would be second. If they consider Livni one of the PM candidates, and if that is how they sold her to the public as part of their agreement, she should be as much involved in the debate as Herzog and Netanyahu would be.

I do not know why she is refusing, and why Hamachane Hatzioni does not want her up there.

As a matter of fact, I think she would do much better in a debate against Netanyahu than Herzog would. Livni is a tough character, while Herzog is a bit wishy-washy and much weaker.

I suspect that the reason is that in a three-way debate either:
a. they are worried that Herzog and Livni would end up contradicting each other in their answers and the public would ask how feasible it is for them to actually work together later, and if this rotation is actually a good idea or not
b. they are worried that Bibi would play them off each other. Livni was right-wing until recently, and Herzog has spoken badly of her in the past. Livni sat in the government and cannot really, even though she acts like she can, abdicate all responsibility for actions the government took while she was a senior partner in it.

I don't know if those are the actual reasons, but a three-way debate seems to make more sense to me than a two-way debate, in this electoral situation, and I do not think Netanyahu is wrong for insisting on it. Let the Labor voters, and other voters, know what they are getting in this rotation deal with Livni.