Why are non-catholics not allowed to receive Holy Communion?
There’s two main reasons:
The Eucharist is the body, blood, soul and divinity of Jesus Christ. We must be properly prepared to receive it (1 Cor 11:26-29). A non-Catholic who does not believe in the Real Presence would not be properly prepared to receive the Eucharist.
Notice the word you used: communion. You are asking why those who are not in communion with the Church cannot receive communion. The word implies a unity and a oneness. Because Catholics believe that the celebration of the Eucharist is a sign of the reality of the oneness of faith, life, and worship, members of faith communities with whom we are not yet fully united are not admitted to Holy Communion.