I can think of two reasons. First, most pre-meds genuinely enjoy science classes, and a biology major gives you a broad science education. Then, a lot of pre-meds believe that being a biology major increase their chance of acceptance to medical school, which is not necessarily true, by the way.
I think you'll be fine as a biochemistry major as long as you enjoy it, and yes, you can major in anything as a pre-med.
I hope this helps!