Because it was the first map of its kind to do the job it needs to do and be so clear. As I have answered to your other question about this, it doesn't matter that it doesn't relate to real geography as long as the connections are clear, so you know from the map how to get to where you want to be. Who cares about geography when you're travelling in tunnels anyway? All I want to know is what line do I need to take to get from A to B, and if I need to change trains to a different line because A and B aren't on the same one, where should I do that? The map tells me that brilliantly.

Giving all the lines different colours also makes it much easier to follow. It has so many design ideas in it that make it just what it ought to be. So it was an inspiration for other underground systems. Have a look at the map of the Moscow Metro and it's obvious where they got the idea from! It just WORKS to do the job it was meant to do and it's hard to see how to make it better. No wonder it's iconic as a masterpiece of design.

Because it's an icon.

A masterpiece of stylized design. It bears no relation to the reality of the geography of the train system but it's easy to understand.

Because it makes something complicated look simple.

Google it you moron