**How did Snape muster the emotional ability necessary to kill Dumbledore?**

In *Order of the Phoenix*, Bellatrix tells Harry that in order to execute an Unforgivable Curse, one has to truly *want* to inflict damage, pain, subjugation, or death against one's victim. 

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> Hatred rose in Harry such as he had never known before; he flung himself out from behind the fountain and bellowed, ‘*Crucio*!’  
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>  Bellatrix screamed: the spell had knocked her off her feet, but she did not writhe and shriek with pain as Neville had – she was already back on her feet, breathless, no longer laughing. Harry dodged behind the golden fountain again. Her counter-spell hit the head of the handsome wizard, which was blown off and landed twenty feet away, gouging long scratches into the wooden floor.  
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>  ‘**Never used an Unforgivable Curse before, have you, boy**?’ she yelled. She had abandoned her baby voice now. ‘**You need to *mean* them, Potter! You need to really want to cause pain** – to enjoy it – **righteous anger won’t hurt me for long** – I’ll show you how it is done, shall I? I’ll give you a lesson –’  
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> *Order of the Phoenix* - page 715 - Chapter thirty-six, *The Only One He Ever Feared* - Bloomsbury
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Yet in *Deathly Hallows*, Snape seems reluctant to kill Dumbledore. While not super high up on the canon ladder, the movie *Deathly Hallows* has Snape saying to Dumbledore, indicating Snape is having second thoughts, "Sometimes you ask too much! Has it ever occurred to you that I don't want to do this [help the cause by killing you] anymore?" (Paraphrase) Dumbledore basically says, "Whether you want to or not is irrelevant." (Paraphrase)

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> ‘After you have killed me, Severus –’  
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>  ‘You refuse to tell me everything, yet you expect that small service of me!’ snarled Snape, and real anger flared in the thin face now. ‘**You take a great deal for granted, Dumbledore! Perhaps I have changed my mind!**’  
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>  ‘You gave me your word, Severus.’  
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> *Deathly Hallows* - page 550 - Chapter thirty-three, *The Prince's Tale* -Bloomsbury
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**If Snape had changed his mind about killing Dumbledore, how was he able to muster the murderous feelings necessary to successfully cast Avada Kedavra and kill Dumbledore?** As Bellatrix said, righteous anger (or being prepared to kill, etc.) was not enough -- one has to actually feel the emotion behind the curse. How did Snape manage to achieve this when it came to Dumbledore?

An answer based on canon (the 10 canon books; interviews with J.K. Rowling; Pottermore) would be fantastic; however, if no canon info is available, a subjective answer within the spirit of canon is certainly more than welcome. :) Please note I completely dislike the HP Wikia; I typically don't consider answers based on, or containing information from, the HP Wikia, as the Wikia frequently contains inconsistent and/or wrong information. Please cite your sources!