This is why I have a love/hate relationship with this game and Bethesda. They make you think twice and some of the quests tug at your heartstrings.
I left him alone due to many reasons. For one, he is indirectly responsible for the salvation of all on Nirn. And thus, their decedents. He could have chose to defy Kynareth/Kyne and help his brother. Some sources say he pitied the mortal races and helped him. Other say it was both Kyne and his pity that made him teach the mortals the words of the dovah/dragons. Nevertheless, he helped when he could have just turned his back.
Two, he went against his own kin. For mortals this is an easy thing. It's seen all the time, brother fighting brother. But dragons have a huge pride. To choose mortals over the dragons is monumental in a dragon's view. It's pure betrayal. Paarthurnax new this but decided to go ahead with it. Against his own brother.
Three, he waited for thousands of years knowing his brother would return. He could have left at any time. Instead he decided to roost there and help the Greybeards with their meditation. When Alduin returned he did not join his brother. He could have joined and pillaged Helgen, Kynesgrove, and others, raised an army with him. But no, he stayed. Another reason I believe he stayed was Alduin was too furious with his brother and I doubt he would let him join after such a betrayal. I think Paarthurnax new this when he decided to betray him. What was the point of betrayal if he wanted to go back? He knew once he made the choice there would be no going back. None. But he did it anyway.
Another reason to believe he should live, is he once again inadvertently saves the world by teaching the Last Dragonborn and helping him find the Dragonrend shout. He even fights his own brother with you once Alduin comes.
When Alduin does die and you return he admits he feels a great loss. Which is understandable. Paarthurnax knew what would happen and accepted it. He also accepts the fact he may return for the real end times. Whatever the case, Paarthurnax always helps you even though he knew what was coming.
I believe this is due to his promise to helping the mortals when he betrayed his kin. Dragons keep their promises due to pride and honor. He fulfilled it to the very end at the cost of his brother and all of his kin. That takes guts.
Of all the lives he did took and due to his name sake, I believe he redeemed himself, in my eyes. He has secluded himself on purpose for a few reasons which are known, indirectly saved the world twice because of his actions, and thus saved thousands of lives. He's the cliche of the bad guy gone good, darkness turned to light. Paarthurnax also admits he has struggled with his inner nature. But he has always prevailed. That's true strength. If one were to question "What if he goes off on a killing rampage?!" He has been there for thousands of years. He could have 'cracked' at any time. Real strength right there.
That's why I always spared him. He pretty much saved the world. What an awesome dragon.