Hezekiah realizes something very simple; God can defend Himself better than Hezekiah can. That leaves Hezekiah in a humble place of depending completely on God.
It is interesting to see Hezekiah reacting in an environment of extreme persecution. Instead of taking it personally, he sees it as an insult to God and asks that God defend Himself. The persecution most of us experience is probably much less intense, but we should still be depending on God rather than our own strength for the response.