I've always wondered why Real Analysis isn't introduced earlier in math education. It might make it easier to grasp concepts introduced in upper-level math.
That's why so many people point to Spivak's Calculus book, since it has been hinted it should be called an analysis text. Strang's Calculus, as do others, start with real-world examples. Personally, I had to do the Strang route, and then come back to Spivak, since I had to admit to myself, I don't have that ability to think 100% abstractly; I need motivation from the real world.