After all these months, I still can't figure out why he's out to kill purebloods. Is it because he wants to protect Yuki and have a peaceful future with her without all these threats around them? An explanation would be much appreciated!

From the newest chapter, IMO it seems that it's related to the woman Kaname met in the past. You must read the flashback where he was in his original body (the ancestor) and he met a woman that using some kind of cloak, right? Nah, it is. But the true wish of that woman or Kaname hasn't revealed yet though

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Yes, as monkry said Kaname is killing Purebloods because of the woman from his past. It's made explicit in the past 5 chapters. To recap:

During a series of confrontations with Kaname over several of the latest chapters, Yuuki manages to get a little information out of him (in between trying to attack him, LOL). In chapter 81, Kaname points out that Yuuki wields the Artemis but still doesn't understand his actions. (All Vampire Hunter weapons have part of the Hooded Woman's spirit in them.) He then states: "Killing Purebloods is 'her' wish." Which causes Yuuki to wonder: "'Her'? Is 'she' that female ancestor?"

In chapter 83, Yuuki confronts Kaname again, and this time she asks him: "What is 'her will' that has compelled you to go this far to accomplish it?" Kaname naturally sidesteps the question...

In short, Kaname's plans have got nothing to do with Yuuki. She may figure into the plans, but she is definitely not the driving force behind them. He confirms this in chapter 80 when he tells Ruka he intends to leave Yuuki behind because she will be a hindrance to those plans. Ruka gets angry at his treatment of Yuuki and also says she can't accept his explanation for why he intends to kill all the Purebloods.

So although we don't know everything, we can safely assume Kaname isn't doing everything he's doing for nice reasons, or for Yuuki's sake. (Given how badly things have deteriorated between Kaname and Yuuki, he'd be shooting himself in the foot if this was how he intended to make the world safe so they can be together!) I think given Ruka's response in chapter 80, it's also pretty safe to say that Kaname isn't acting for the greater good in killing all the Purebloods. My guess is he's doing all of this for personal reasons.

So yeah Kaname's motives are still partially a mystery; however, chances are good that Ruka will reveal what Kaname said to her about his reasons sometime soon. Hopefully...

Well, you have an answer for that in chapter 89. Go read it.
(But beware for YukixZero fans, this is my warning)
He explained it a lot and very clearly. He's not a bad person

No, but he's still a manipulative bastard that uses people for his plans regardless of how much it hurts them. And Yuuki is thoughtless as she doesn't even seem to care that one of those that he's used and caused pain was Zero, himself. How am I supposed to believe she has any feelings for Zero if she doesn't even show any concern or waivering over the fact that Kaname caused Zero such pain.

As a Zeki fan, after this chapter, I no longer want it to happen in canon as Hino-sensei has ruined it's believability. I hope he ends up with Yuki's best friend so she'd have to see him being happy with someone else.