“He himself went on before them, bowing himself to the ground seven times, until he came near to his brother.”
Short answer
The Church teaches that adoration belongs to God alone and that no man may receive it. Scripture records bowing and kissing as signs of honor between people, with no idolatry in them, and it also records worship being refused. The text says that Cornelius worshiped Peter, and that is what Peter refused. Honor shown to a pastor because of his office is a different act from worship.
Drafted from primary sources. Every quotation is checked against the page it links to.
13 quotations in date order
“And they told the king, “Here is Nathan the prophet.” And when he came in before the king, he bowed before the king, with his face to the ground.”
“When Peter entered, Cornelius met him and fell down at his feet and worshiped him. But Peter lifted him up, saying, “Stand up; I too am a man.””
“But we beseech you, brethren, to respect those who labor among you and are over you in the Lord and admonish you, and to esteem them very highly in love because of their work.”
“And they all wept and embraced Paul and kissed him,”
“…behold, I will make them come and bow down before your feet, and learn that I have loved you.”
“…I fell down to worship at the feet of the angel who showed them to me; but he said to me, “You must not do that! I am a fellow servant with you and your brethren the prophets, and with those who keep the words of this book. Worship God.””
“It is well to reverence both God and the bishop. He who honours the bishop has been honoured by God”
“But that service which is due to men, and in reference to which the apostle writes that servants must be subject to their own masters … is usually designated by another word in Greek, whereas the service which is paid to God alone by worship, is always, or almost always, called λατρεία in the usage of those who wrote from the divine oracles.”
“For as for me, I do not seek to be prospered by words but by my conduct. Nor do I regard that as an honour whereby I know that my brethren lose their honour. For my honour is the honour of the universal Church: my honour is the solid vigour of my brethren. Then am I truly honoured when the honour due to all and each is not denied them.”
“…the reverence which we pay to God, and which belongs to latria, differs from the reverence which we pay to certain excellent creatures; this belongs to dulia … And since external actions are signs of internal reverence, certain external tokens significative of reverence are offered to creatures of excellence, and among these tokens the chief is adoration: yet there is one thing which is offered to God alone, and that is sacrifice. … Accordingly it was with the reverence due to an excellent creature that Nathan adored David … It was with the reverence due to God that John was forbidden to adore the angel”
“Adoration is the first act of the virtue of religion. To adore God is to acknowledge him as God, as the Creator and Savior, the Lord and Master of everything that exists, as infinite and merciful Love. "You shall worship the Lord your God, and him only shall you serve," says Jesus, citing Deuteronomy.”
“God has willed that, after him, we should honor our parents to whom we owe life and who have handed on to us the knowledge of God. We are obliged to honor and respect all those whom God, for our good, has vested with his authority.”