Short answer: You do not share the Catholic faith enough to join the Catholic Church, so you should not be receiving Communion in the Catholic Church.
Long answer: There are a variety of reasons why you should not receive, beginning with the one listed above. But a reason that may be understandable for you where you are right now is the matter of personal integrity.
Say you move to a foreign country but do not choose to become a citizen. Should you attempt to vote in that country’s elections? Why or why not? Say a non-American moved to the U.S. but did not become a citizen. Should that person take it upon himself to attempt to vote in American elections? Why or why not?
Just as voting is a privilege of citizenship in a country, Communion is a privilege of citizenship in the Church. By presenting yourself for Communion, by your actions you are giving the impression that you are a Catholic who holds to the Catholic faith. If you are not a Catholic, your actions are therefore false and you undermine your own personal integrity.
It may also help to understand a couple of the reasons why the Church reserves Communion to Catholics. It is not to deprive people of Christ, but to protect Christ’s body and blood from sacrilege and to protect people from the consequences of unworthy reception of the Eucharist (cf. 1 Cor. 11:27-30).
Analogously, most reasonably intelligent and physically coordinated people are capable of driving, some before they reach the minimum age. The state, however, requires testing and licensing before allowing people the privilege of driving. This is done not because the state wants to deprive people of access to driving, but in order to protect them and to protect society from those who have not demonstrated the knowledge and skill required to drive safely.
In like manner, the Church requires that only Catholics receive Communion because it protects the Eucharist – the very body, blood, soul, and divinity of Jesus Christ – from the possibility of abuse by those who do not know better, and because it protects the people themselves from the possible consequences Paul outlines for unworthy reception of the Eucharist.