Thomas Aquinas puts it this way, a living body has both blood and particles of flesh in the blood, and blood in the flesh, so if you receive one you receive both. He also makes the argument that drinking from a common cup has a certain repugnance to it that should not be associated with Holy Communion, as well as the fact that it can be spilled.
Thank you. Reminds me of Shakespeare’s Merchant of Venice, where the person was entitled to take his “pound of flesh” but not any blood, and that was impossible to do.