A friend recently suggested to me that we should perhaps tell students earlier what she was told by her professor in Germany only in her third year or so.
The most important thing you learn at University is how to learn.
This applies to all subjects, I think. In a particular subject, you might be able to specify this a little more. You (should) learn how to think about problems, how to find enough material to understand a new problem, how to deal with lots of material, how to work to deadlines, … You learn how to persist on hard topics/problems, you learn how to think creatively, and in maths you certainly (should) learn how to think logically, how to make a proper logical argument, the importance of making the right assumptions and of knowing your assumptions, and so on. In Science I think you learn how to deal with data, what you can and can’t learn from data, etc.
Of course you also learn some facts. You can’t teach someone mathematical argument without given them some specific mathematical arguments in a specific subject. And yes, the material you learn in the first year or first few years will be relevant to (some of) the courses later on. And yes, if you want to stay in maths, you need some of the actual knowledge you have learnt in certain areas. But much much more, and no matter whether you stay in maths or go and do something else, you will need to know how to think for yourself, how to tackle problems, to be creative in your thinking, how to question things, etc.