u/Hairy-Art9747

I know that gravity isnt a force that actually pulls things but is rather the curvature of spacetime around massive objects. So when the Earth revolves around the sun, earth moves toward the sun because the space that earth is moving through curves toward the sun. But what confuses me is the fact that the sun is also moving through the universe as it revolves around the center of the galaxy. So earth isnt just falling towards the sun, its also being pulled through the universe as it follows the sun. But if gravity isnt a pulling force and earth is just falling towards the sun, why does the earth follow the sun around the galaxy?