Why did Jack run away after giving Elizabeth a compass in Pirates of the Caribbean 2?

Because Jack's compass is special, it can point out the direction for what one wants most in his heart.

At that time, everyone wanted Neptune's heart, so Jack gave Elizabeth the compass, hoping that she would hold it in her hand and point out the location of the heart.

Why did Jack run away? Because what Jack wanted most at that time was not the heart of Neptune, but Elizabeth!

So, with the compass in his hand, he couldn't find the heart of the siren.

Do you understand, my friend?