To cast an Unforgivable, you have to mean it. You have to want to cause pain.

Severus Snape is to murder Albus Dumbledore tonight.

He stands there, staring at the headmaster, knowing he has to kill him. It is not just his job, it is expected of him, by the old man himself.

So he focuses on his hatred.

He hated James Potter. He hates his son.

But he doesn't just hate Harry Potter for looking like his blasted father. He hates him because she died for him. Lily, his Lily, had died so that wretched brat might live.

If he tries, he can even hate Dumbledore. He can blame him for her death.

She wouldn't have died if he really had been omniscient. He made a mistake. The infallible Albus Dumbledore made a mistake, and she paid the price.

It makes the curse easier to summon.