Why is only dragonglass/fire able to destroy White Walkers?

Question

Jon Snow explained to Cersei in Game of Thrones that they can only destroy White Walkers by using dragonglass or burning them with fire.

Why do only dragonglass (and fire) have the power to destroy the White Walkers?

Answer 1

Why is only dragonglass used to destroy White Walkers?

It isn't, we have two known ways of destroying them, with a possible third option.

Dragonglass

Valyrian steel

It is also speculated that dragon fire can kill White Walkers but we don't know if it can yet.

We also know that normal fire cannot kill White Walkers as the flames seem to pass when they get near.

Why do only dragonglass (and fire) have the power to destroy the White Walkers?

We don't know, they are magical and were created by the Children of the Forest by plunging a dragonglass dagger into the heart of a First Man but we don't know why only those items can kill them.

As for fire, we know it can't kill them but it can kill wights. This is what Jon was talking about in his demonstration to Cersei, not White Walkers. If this wasn't clear already the official script makes it clearer:

The Hound chops an arm off at the elbow. The arm keeps flexing and grasping.

The demonstration shakes Cersei in a way few things can.

And though Tyrion is seeing this for the first time as well, he spends more time watching Cersei than he does watching the wight itself. Noting her reaction.

Everyone who has never seen a wight is shocked as well.

Everyone except for Qyburn, that is, who steps forward to pick up the still-moving hand and forearm, and beholds it with fascination.

With a flint, Davos sparks a torch and hands it to Jon.

He takes the hand from Qyburn, ignites it and drops it. The hand dies.

JON: We can destroy them by burning them. (beat) And we can destroy them with dragonglass.

He draws a dragonglass dagger.

JON: If we don’t win this fight, then that...

He points to the wight’s torso as it crawls toward him with its single arm.

JON: ... is the fate of every person in the world.

When the wight’s torso reaches him, he picks it up by its remaining wrist, and stabs it with the dragonglass. It deanimates and falls to pieces, ending the demonstration.

_{Game of Thrones, Season 7 Episode 7, "The Dragon and the Wolf" - Official script}