The Doctor is well aware that he comes across as an irascible, crotchety old man, but how else is he supposed to act around these humans? In some ways he’s just behaving the way they expect him to. He looks like an old man, and indeed is old by their standards though still young by his own, so he treats them like the children they are.
He’s impatient with them, orders them around, because dealing with such primitive intellects is frustrating. There’s so much they don’t understand. But at least they’re trying to learn and that counts in their favour.