That's true, but a lot of people think the school you attend matters. For example, in the context of hiring, if you have 2 otherwise candidates but you can only choose one, most people would choose the person who went to Stanford over the guy who taught himself to code or attended a lesser respected school (in most cases). Some companies are stupid enough to only hire people from fancy schools. I think Google did something like this for a while, but thankfully they stopped.

Thus, attending a fancy school is a big advantage if you've got the money or have another way to get in.