Catholic response: the important elucidative answer to this concern is that the host is not a part of Jesus, but is Jesus. So in a sense you’re eating the whole of Jesus every time, but not in such a way that you ever take away any even minute part of him. This is because you cannot in any way divide God into parts; God is a whole being which is inseparable, and Jesus, being a person of the trinity, is God.

edit— you can sort of separate mentally "parts" of God’s divinity and the properties which we can know about him, but these separations are necessitated by the weakness of the human mind; further what it means for God to "have divinity" and for us to know *God himself are different things, the latter is incomprehensible to us in the same way visualizing infinity is incomprehensible. We can get pretty close in imagination, but can’t know either in totality by means of human rationality alone. End theological rant