What can I do if my computer will not update to big sur

Select the Apple () menu > About this Mac, and compare the contents in parenthesis on that panel's product description line to macOS Big Sur is compatible with these computers - Apple Support. If your Mac is not among the compatible models, then you cannot upgrade to Big Sur from Catalina. You will need to continue using Catalina, or consider a newer (or Apple refurbished) Mac to qualify for a newer operating system.