“When meeting with my counselor, she said dropping this class would take me out of the runnings for top schools and things such as premed and business degrees.”
I think what your GC is telling you is that if you drop down a level in math, the evaluation that GCs send into colleges will not include the coveted ‘most rigorous schedule’ evaluation of your transcript that the most selective schools expect to see. That doesn’t mean that you can’t get admitted to many excellent schools with strong reputations - but if you apply to the highly selective schools (acceptance rates of lower than, say 15% to pick a random cut off), you will be compared to your peer with the ‘most rigorous’ rating, and you are at a disadvantage. As for the threat about pre-med and business degrees - that’s sheer nonsense. First of all, there is no such thing as a pre-med degree. If you want to be pre-med, you need to take certain classes, one of which is going to be calculus - and you will need top grades across the board. But you can be pre-med almost anywhere and medical schools don’t care where you go as long as your overall grades and MCAT score is high. Things a a bit different for business majors - but you don’t have to have calculus in high school to be a business major at a reputable school.
Assuming you aren’t hooked on the prestige of a ‘highly selective school’ (and you shouldn’t be), there is a good case to be made for taking the lower level math class. For one thing, math is something that requires a very solid foundation on which to build. Taking a bit longer to make sure you really have it nailed, is a good idea. Secondly, while you could muscle your way through the course with lots of tutoring and assistance, if this is going to be at the expense of your other classes, and your overall quality of life, it might not be a worthwhile trade. Only you can decide how much stress you want in your life. It does not indicate a lack of work ethic or character or commitment to say ‘no thanks’ to doing it the hard way. Third, there is no calculus on the SAT, so the lack isn’t going to show up on your test scores.
And by the way, it’s not an all or nothing decision either. You can stick it out for freshman year (when a lower grade or two tend to be forgiven), and see if you want to continue next year. As kids mature, they often find that some of the more abstract thinking that goes with higher level math actually starts to come more easily to them - be open to that possibility as well.