You can legally carry meat into the BVI.
From the BVI Tourism site:
Visitors coming from the North America with meat products for consumption during their stay will not have to fill out the application, if they are bringing less than 40LBs of meat.
As for why to take food with you, the two main reasons people give are it’s cheaper in the mainland US and it’s easier to prepare in your home kitchen. We bring down a soft sided cooler of food – mostly meats and main dishes – so that we can prepare them at home. (We marinate or cook and then vacuum pack them. We carry the cooler full of frozen food with no ice and check it as a bag.) We have fun planning for our trip while we are cooking at home and then spend less of our vacation time cooking.
We put together a more detailed post of how to plan food for your trip focused on shopping while you are there.