In the allegorical words of the Lord there is much that clarifies this question. It stood before the Church for urgent resolution because of the universal purpose of the Gospel.
For everyone remembered the Lord's word: preach the Gospel to every creature, Mk 16:15.
But now the Apostle Peter finds that many creatures are unclean. Why? Because, according to the law of the Old Testament, some were recognized as fit for use, and others as unfit.
Yet the same Lawgiver, God, declares that when He has cleansed anything, it can no longer continue to be regarded as unclean.
Consequently, when it was commanded that the Gospel be proclaimed to every creature, then it must be preached to all.
Those who accept this preaching must no longer be considered unclean, but must be received into communion equally with the Jews.
The miraculous character of the appearance, and the threefold instruction, certainly had to lead Peter more deeply into the meaning of the vision.
He had to understand that it was not to be taken in the ordinary sense of food. What he saw descended from heaven and was raised there again as something immaterial and spiritual.
Therefore it had to be considered spiritually.
The command to the Apostle to arise is significant. He was either praying on his knees, or, seeing heaven opened and what descended from it, he fell on his face.
So the Old Testament prophets did at especially overwhelming visions; see Dan 10:9.
The adaptation of the vision to Peter's felt hunger is also significant. It shows that, when eating food, one must firmly remember that man does not live by bread alone.
It is good to share food with the one most in need of it, verse 23. Still better is it to share spiritual bread.
According to blessed Theophylact, "Peter, the first of the Apostles, needed a divine revelation concerning the calling of the Gentiles to the Christian faith.
For he did not know that circumcision and uncircumcision make no difference in relation to faith.
Certainly he did not clearly know that the Lord had said that, when service through faith was revealed, the Gentiles also were to be taught that faith.
They did not know this until His ineffable will, through this appearance, revealed the mysteries."
"The vision occurred three times as a sign of the undoubted truth of what was communicated in it, and to assure Peter of the unchangeable divine decree concerning this matter."