Dumbledore values his morality more than the greater good.
Creating Horcuxes requires one to kill. In Dumbledore's (and others') view this is a terrible moral crime. In Chapter Eighteen of Half-Blood Prince we get the following description:
"All I could find was this, in the introduction to Magick Moste Evile — listen — 'Of the Horcrux, wickedest of magical inventions, we shall not speak nor give direction....' I mean, why mention it, then?" she said impatiently, slamming the old book shut; it let out a ghostly wail.
Later in Chapter Twenty-Three Slughorn describes it as requiring the most evil act:
"But how do you do it?"
"By an act of evil — the supreme act of evil. By commiting murder. Killing rips the soul apart. The wizard intent upon creating a Horcrux would use the damage to his advantage: He would encase the torn portion —"
And when questioned further by Tom Riddle he reiterates the horribleness of creating Horcruxes:
"Merlin's beard, Tom!" yelped Slughorn. "Seven! Isn't it bad enough to think of killing one person? And in any case... bad enough to divide the soul... but to rip it into seven pieces..."
In Chapter Thirty-Five of Deathly Hallows Dumbledore himself refers to murder as "unspeakable evil":
"You were the seventh Horcrux, Harry, the Horcrux he never meant to make. He had rendered his soul so unstable that it broke apart when he committed those acts of unspeakable evil, the murder of your parents, the attempted killing of a child.
Now one could argue that the greater good would have been served by Dumbledore remaining alive, but it is unlikely that Dumbledore would have sacrificed his morality in order to achieve this. Consider all the other times that Dumbledore had the opportunity to commit an immoral act, an act of unspeakable evil, etc. and he chose not to even though the greater good would have been well served by it. Particularly in Order of the Phoenix he had a dozen of Voldemort's top Death Eaters at his mercy. Had he simply killed them all instead of capturing them, who knows how many innocent lives would have been spared (from the future killings performed by those Death Eaters once they escaped)? If Dumbledore (and others on his side) had always fought to kill, perhaps the entire war could have been averted.
As for why Dumbledore places morality above the greater good, it is likely based on the experiences of his youth. At that time he was friends with Grindelwald and together with him championed the cause of the greater good. But eventually he realized that the greater good sometimes creates fuzzy lines, and one false move can throw you over the precipice of morality from which you might never return. Indeed, one could argue that Dumbledore spent the rest of his life trying to avoid becoming Grindelwald, and therefore he never killed anyone even if the circumstances could justify it.
Note the following exchange in Chapter Thirty-Five of Deathly Hallows:
Dumbledore turned his whole body to face Harry, and tears still sparkled in the brilliantly blue eyes.
"Master of death, Harry, master of Death! Was I better, ultimately, than Voldemort?"
"Of course you were," said Harry. "Of course – how can you ask that? You never killed if you could avoid it!"
"True, true," said Dumbledore, and he was like a child seeking reassurance. "Yet I too sought a way to conquer death, Harry."
"Not the way he did," said Harry. After all his anger at Dumbledore, how odd it was to sit here, beneath the high, vaulted ceiling, and defend Dumbledore from himself. "Hallows, not Horcruxes."
"Hallows," murmured Dumbledore, "not Horcruxes. Precisely."
Here Dumbledore considers the actions of his youth to be almost on par with Voldemort. He is only somewhat comforted when Harry reminds him that he spent the rest of his life avoiding killing. That, in Dumbledore's mind, is his penance, and he would be unlikely to sacrifice that to remain alive.
Later in that conversation Dumbledore tells Harry that he never trusted himself with power after that (my emphasis):
"Years passed. There were rumors about him. They said he had procured a wand of immense power. I, meanwhile, was offered the post of Minister of Magic, not once, but several times. Naturally, I refused. I had learned that I was not to be trusted with power."
"But you’d have been better, much better, than Fudge or Scimgeour!" burst out Harry.
"Would I?" asked Dumbledore heavily. "I am not so sure. I had proven, as a very young man, that power was my weakness and my temptation. It is a curious thing, Harry, but perhaps those who are best suited to power are those who have never sought it. Those who, like you, have leadership thrust upon them, and take up the mantle because they must, and find to their own surprise that they wear it well.
Killing people would be precisely the power that Dumbledore would not want to trust himself with. He might start out with good intentions but end up as another Grindelwald or Voldemort. Any foray into such areas of magic would carry the danger of reigniting the immorality of his youth, something he had worked very hard to repress. Indeed, this can perhaps be likened to the reason Snape gives for why Dumbledore wouldn't let him be the Defense Against the Dark Arts Teacher:
"Not quite," said Snape calmly. "He wouldn't give me the Defense Against the Dark Arts job, you know. Seemed to think it might, ah, bring about a relapse... tempt me into my old ways."
So in short, Dumbledore would have found the notion of killing and creating Horcruxes to be abhorrent, and to go against what he had spent his life working towards.
Additionally, the process of "dying", existing as "less than a spirit, less than the meanest ghost", and then regenerating a body is not exactly a picnic. As Slughorn described it in Chapter Twenty of Half-Blood Prince:
"... few would want it, Tom, very few. Death would be preferable."
