Focus on how much your DD or DS will gain by going away to BS - if that is what they want and are ready for that school experience. We have all been there @ChoatieMom says.
Today, BS is more “collegiate” than almost any college we know. Your kiddo will have an exceptional life changing experience. At least for us, there is no way we could give our kiddo the type of education and life experience here at home. There are some parts of the country where parents have the choice/opportunity of excellent local schools and intellectually stimulating environs. We told our kiddo that there is a big beautiful world out there.
The hard part now is when kiddo returns home. It’s a small & narrow place in our hometown. So, I think you (as a parent) will feel better when your kiddo attends a Revisit, meets new students from around the country and around the world, and experiences new opportunities.