Why didn’t Harry talk Parseltongue to the basilisk? Good question. There are a couple of times in the books where Harry seems to ignore the obvious solution. Another great example is when he was stuck in the trick stair, under his invisibility cloak, when the egg was screeching and he dropped the Marauder’s Map. There it lies almost within his grasp, and he never thinks to use a Summoning Charm to retrieve it. Why is that?
There’s actually a perfectly good solution to this mystery: he’s a kid, facing unimaginable danger or major stress, and he just doesn’t think it all through. It would actually be less realistic if he always had the right spell on the tip of his tongue, sort of like the way James Bond always has the perfect gadget at the right moment. Harry isn’t a superhero. He’s a kid, who manages to survive and even win while making mistakes and floundering around, just like any kid (or grownup, for that matter).
What sets Harry apart is his sense of purpose and mission in his life. He hasn’t really come to terms with it yet, but it’s clear that he subconciously sees himself as something Special. I don’t mean that in a bad way at all. Harry senses that it’s up to him, that he just doesn’t have a choice but to place himself in the path of danger. It’s his destiny, and he knows it intuitively. Everything does seem to happen to him. That’s the way things are, and he knows it.
But he doesn’t have all the answers yet. He’s still a kid, in training. A trained wizard is not just one who knows all the right spells, but one who remembers the right spell to use at the right time. In all his adventures, he’s really been helped along to victory almost every time. He didn’t think of the ways to defeat the dragon or swim the lake. He wouldn’t have been able to defeat Voldemort in the duel except for the fact that his wand was a mate of Voldemort’s. There is destiny there, true, so it’s not just blind luck, but it certainly isn’t anything Harry personally did or decided.
Harry Potter, we are coming to realize, is the key to something big. He’s extremely important to everyone in the wizarding world, both the “good guys” and the “bad guys.” Even the centaurs of the Forbidden Forest know it. He is only beginning to realize the role he is destined to play in the great saga. He is also just beginning to come into his own as a wizard.