When you assume something, you believe that to be the case, even though you cannot prove it. For instance, people might make the assumption that someone does not eat much because he or she is thin, even though that does not have to be true.
In this statement, the speaker is assuming that those people who argue that embryos are human beings give more importance to those "cells" than to the health of living people with illnesses such as Parkinson that could benefit from them, and therefore do not support the use of discarded embryos on research against those diseases, and that is not necessarily true.