In the latter case he must have valued Harry instrumentally more than himself, as he said before that he would not be deterred by hostages. (Though he could, of course, have been bluffing.) That seems somewhat odd though, given that Harry is currently unarmed and at the mercy of Voldemort.

Remember that Dumbledore is truly willing to sacrifice himself, and he has access to a number of prophecies. He likely knows that this is the right call, both by his altruistic morality and whether or not it will lead to Voldemort's defeat.

(He also probably correctly thinks it is more likely that Harry can rescue him from being frozen than he could rescue Harry.)