[HonorInPa]

Simple, Jesus said, at the Last Supper, “this is my blood of the covenant which is poured out for many.” He didn’t say “poured out for Catholics only”.

[Zathras]

It was also about Jewish Passover.

[AnAmericanMother]

But He did not say "for all" - by the way a recent point of contention, corrected in the new English translation.

The general teaching is that receiving in the Catholic Church is also an acknowledgement that you agree with the Church's teachings and are in good standing and (most importantly) NOT in a state of mortal sin.

And Catholics are not the only body with "closed communion" - quite a number of Baptists and some other Protestant denominations (e.g. LCMS) have the same practice.