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Madam Pomfrey is Hogwarts's mediwitch. In other words, she's the magical equivalent of the school nurse. She is very practical, down-to-earth, and a little brusque. But her heart is clearly in the right place. After Professor McGonagall has been stunned by Aurors chasing Hagrid, Madam Pomfrey says indignantly:
I don't wonder you're shocked, Potter [...] As if one of them could have Stunned Minerva McGonagall face-on by daylight! Cowardice, that's what it was ... despicable cowardice ... if I wasn't worried what would happen to you students without me, I'd resign in protest. (32.15)
Madam Pomfrey genuinely cares about her students and respects her colleagues. In fact, if there's one silver lining to the whole Professor Umbridge episode, it's that all of the Hogwarts teachers and staff (with the gross exception of Argus Filch) have shown what excellent people they are.