As others have noted, to receive the Holy Eucharist is more than “receiving communion.” In fact, the name alone should indicate why non-Catholics are not permitted to receive the Eucharist–their views are not in sync, or in *communion *with the Catholic Church.
There is another important reason, too. By denying the Eucharist to those not in communion, the Church is preventing non-Catholics from committing blasphemy, as noted by St. Paul in
1 Cornithians 11:17-28. In that passage of Paul’s letter, he warns his readers that partaking of the Body and Blood of Christ without accepting its full weight would lead in disaster (in fact, in the same passage, he notes that several people who had taken the Eucharist without proper discernment were ill or even dying).
So, please do not take it personally. I would invite you to contemplate more on what the Eucharist truly means for Catholics. We do not see it as a symbol. He is there, and we would do well not to share it with those who do not yet fully understand the mystery that is transubstantiation.