The Eucharist is the Body and Blood, Soul and Divinity of our Lord Jesus Christ.
This is basic stuff in Catholicism.
As such, a consecrated Host - the Eucharist - is not an article of property. You can't own the Body and Blood, Soul and Divinity of our Lord Jesus Christ. The very idea is absurd and contrary to every teaching on the Real Presence. No human can assert ownership over Jesus as if He were mere chattel.
An unconsecrated host, being merely a kind of bread, can and is property. But once it is consecrated it is no longer possible to be a species of property. And to claim that the Host still is property and that can be owned - that anyone can own the Body of Christ, the Divinity of Christ - is among the highest kinds of hubris that one can imagine.
Clearly, anyone who would claim that the Eucharist is property capable of being owned is either a heretic of the grossest kind or he is someone who really hasn't quite thought through the ramifications of his too-cute-by-half argument.