As I remember from the text books, lift makes a plane "go up". Changing the pitch of the aircraft using the elevator simply changes the lift produced by the wings by changing the angle of attack. Saying thrust makes a plane "go up" is a fallacy in a sense. You can still climb at idle throttle, albeit for a limited time.

Of course one can argue that thrust makes and F-18 climb vertically, but this is not what is being discussed.