What did Jesus mean by saying we should not strive to belong to this world? He was not telling us to down-play our complete dependence on the air, food, and social contacts that make up our worldly atmosphere.
Obviously, he was contrasting the value we put on life in this world with life in the next. And, to put value in the next life takes more than letting out heads swim in the clouds. What it takes are efforts to bring ourselves and others to measure up to what God planned for us in creating us.