The refusal of Saul's armor could be seen as a refusal of Saul's kingship.
God will be more greatly glorified when an unarmored man kills the Philistine's champion.
The pre-battle exchange makes clear that David has faith that the battle is won not by him, but by the LORD (vv. 45–47).
David kills Goliath with a single stone from a shepherd's sling (vv. 49–50), then uses Goliath's own sword to take his head (v. 51). The weapons of the destroyer are used against the destroyer.
Israel yet again inherits a victory they did not begin, similar again to the victory gained by the actions of Jonathan and his armor-bearer.
David fights as the representative champion for a people who cannot defeat the enemy themselves.
He enters the conflict not with the weapons of the world but with something the enemy despises.
His people inherit what he won. He goes first; they follow.
The enemy's own weapon turned against him points to Christ, who destroyed death through death, rendering powerless the one who held the power of death (Hebrews 2:14).