It is not Castiel's blind faith that grates on Raphael; such faith is foolish, perhaps, but not objectionable. What cannot be accepted is the actions he uses it to excuse.
He has heard about humans who commit the worst atrocities, turn on their own people and claim that it is God's work - as if the God Raphael followed would have condoned such actions - and he wonders whether Castiel knows these stories.
Of course, Raphael thinks irritably, he spends so much time down on Earth with those children; he must know far more about their ways than I do.
Raphael looks at the evils that humans perpetrate against their own people and his heart aches for his Father, his Father who would never have allowed such things to happen and so, logically, is no longer present to put an end to them. Castiel, apparently, watches Earth's inhabitants slaughter their brethren in the name of God's will and thinks it would be fun to try this at home.
Seventeen angels dead this week, Raphael's lieutenants tell him. Before that man (the righteous man, oh, the irony) gave up so easily, after only thirty years - a flickering moment of pain was all he could endure, to Raphael's eternal contempt - and the seals began to be broken, not a single angel had died since Lucifer's Fall. Six thousand years they had all lived in peace, serving first God and then the rules God had left them, and had Castiel not turned his coat to follow the petulant demands of children rather than the orders of his superiors, their enemies could have been vanquished, their Paradise could have been built, and their peace could have lasted forever. But Castiel betrayed Heaven, corrupted by the mayfly weakness of the humans with whom he associated, their talk of freedom and choice; and now another celestial war begins, a second Satan begins to rise under the power of his own arrogance, and it falls to Raphael to defeat him. Lucifer, at least, was an archangel, could justify his pretensions to power. But Castiel? He came of one of the lowest choirs, and while the foolish angels who follow him for his charisma and his lies look at his newfound, Hell-given power and forget his rightful place in Heaven's order, Raphael does not. Power is important, of course, but there are more important things: Castiel's fate was to serve, and he had no right to rebel against what was ordained for him.
Raphael is the last remaining archangel. Without arrogance he knows that it is his responsibility to lead Heaven, to rule as his Father's successor. He will cede power to Michael if Michael can be recovered - not gladly, perhaps, for Raphael enjoys power; but he will do it, because Michael is stronger, Michael is older than him, Michael is destined to rule, and it would be right - but he will never, not in a thousand millennia, allow Castiel to take his place.
Raphael feels pity for the angels Castiel has turned to his service, if not for their leader, but he will not allow it to cloud his judgment. He does not want to kill them, he does not want to add to the chaos and the destruction, but he has no choice; he will send out his loyal soldiers to slaughter their less steadfast brothers because it is his duty. Their deaths will be at his hands or the hands of his warriors, but their blood will not stain Raphael's conscience. The deaths of Castiel's angels are to be regretted - no matter how misguided or malevolent, they are Raphael's brothers and God's children - but ultimately it is the fault first of their treachery, second of their gullibility, and third of their lying leader.
We all must meet our fates, Raphael thinks. God is dead, and all we can do now is follow the orders He set down as our destinies. We all must meet our fates, and if Castiel's must be forced upon him then yes, it is a shame, but it must be done. Raphael's fate is his responsibility and his power, and he intends to meet it with dutifulness and dignity.
Castiel has to die. Raphael has to rule.
This is the way it has to be.