You know, that's the biggest misconception about mechanical engineering. Many people think that since it has the word "mechanic" in it that it means it's all about cars. While it's true that you can definitely go the automotive route with it, mechanical engineering is much more diverse. Everything around you: mouse, keyboard, desk, the chair you're sitting on.....all required a mechanical engineer to design.

Your dad is totally right though, if you go into mechanical engineering you'll definitely have opportunities to work with cars. One of the major racing teams had their champ car(looks like a small Formula car) at my school yesterday. Talk about engineering. The whole body was carbon-fiber! The control arms for the suspension were shaped like an airfoil (wing) instead of just round tube to reduce drag. Pretty amazing stuff.