First the question is not correct. A Bishop or priest is the ordinary minister of the Eucharist. To answer that question there are two ways - the short way and the long way. Here is the short way.
In the Church, as it is the mystical body of Christ, there are different parts of the body that have different functions just as in a natural body. In the economy of salvation God has established a ministerial priesthood that has the power through Christ to confect the Eucharist. This power is given in the Sacrament of Holy Orders on the level of priest and Bishop. These persons are deputed to function at the altar of the Lord and offer the one sacrifice of Jesus Christ commemorated on the altar of every mass as was commanded by the Lord. This Sacred Character that the priest and bishop receive in Holy Orders changes their soul similar to the effect of Baptism in such a way that if conforms them to Christ in His Eternal Priesthood. By this molding of the priest or Bishop to Christ he is then disposed to receive the necessary power to effect the Eucharistic Sacrifice. This is what is meant when we use the term 'in persona Christi."
The short answer might be, changing matter into the body and blood of Christ is an enormous, a cosmic thing. It is only entrusted to a special order of men, and it has been so as far as we know and believe from the beginning. If I said those words over the elements and believed I had effected a transubstantiation, it would be not only sacrilege, but delusional behavior that ought to get me sent straight to a psychiatric hospital.
Even protestant denominations, many of which deny the real presence in the first place, do not allow just any lay person (as they define the difference between lay and clergy) to say what they often call the “words of institution.” That always requires an ordained minister. They are not performing a valid sacrament, but they do seem in some way to get this point.
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