Why shouldn't I take a Biology and Math class at the same semester?

Your cousin & her bf don't know what they are talking about. No reason not to take a biology course & a math course in the same term. Ditto for any science & any math courses. You take the courses you need to meet general education/distribution requirements to graduate, prerequisites for your major or a future course you want to take, etc. You want to graduate, don't you? And not take umpteen years to do it, right?

It is very common for science majors, premeds, etc, to take science & math courses in the same term, even multiple science & math courses. E.g. a first term freshman aiming for a major in one of the sciences to take Intro Biology, Intro Chemistry, and Calculus first semester (plus a couple other classes).

Both may be very challenging by themselves, much less in the same semester.

With regard to physics, you're right about the math requirement, which is usually calculus, unless the specific physics class mentions that it's "non-calculus" based, which usually still requires one to be adept in algebra & trig.

Lots of people take such classes at the same time. You may be a better student than your cousin and her boyfriend. Ignore them.

Unless one is a prerequisite of the other, you can take them both at the same time.

If math is a prerequisite for biology (and I -really- don't think it is) then you have to take the math class first (if you were allowed to take them in the same semester, it would be called a "co-requisite" not a "prerequisite").

Math is often a prerequisite (college algebra) or corequisite (calculus) for physics, but rarely for introductory biology. When you get into some intermediate biology classes, like population biology, they may require statistics or calculus, but not, in my experience, intro classes.

You could, unless bio requires a math class as a pre req, you can take them at the same time, and if there is no pre req, there shouldn’t be math that a freshman wouldn’t know.