Why can't non-Catholics receive Communion at Mass?

Receiving Holy Communion signifies full ecclesial communion with the Catholic Church. Because non-Catholics do not share the same faith, sacramental life, and governance, receiving the Eucharist would misrepresent a unity that does not yet fully exist. Catholics themselves must be in a state of grace to receive worthily (CCC 1415).

The Eucharist as the Sign of Full Ecclesial Unity

Reception of Communion by those not in full communion would thus obscure rather than celebrate Christian unity, treating a wound in the Body of Christ as though it were already healed.