Of course a counselor will tell you to take all those other classes, they are employed by the college and most likely instructed to push classes on students. But it's not a bad thing. Take the classes.
That being said, having a pysch, math, English, world history, etc etc will not necessarily make you a better EMT, but in my honest opinion, they will. Psychology will teach you how to understand people and their feelings/actions better. That will help you better treat them. Math is a no brainer since math is a big part of medications, you would not want to make mistakes there. English is always good since we speak it. The smarter and more professional you talk, the better a patient will trust you.
The only person you have to listen to, is yourself. If you want to be an EMT, go be an EMT. No one can tell you what you should do with your life.
My advice is, do what you want. Learn as much as you can even if it "isn't in the field".