This is a very deep response, and I’m very glad that we get to make it again. (I mean, sheesh, everybody else in the Catholic world always said “And with your spirit.” It’s not what they said in the official Latin (“Et cum spiritu tuo”), or the Spanish (“Y con tu espiritu”), or any other language. We English speakers were the odd ones out, with our crazy insistence that “And also with you” was the same as “And with your spirit”.) (Though of course, if you really think it’s the same exact meaning, saying “And with your spirit” will be exactly the same as what you say now, and so it will be easy for you for change to it. Yay!)
2 Timothy 4:22 — “The Lord Jesus Christ be with thy spirit. Grace be with you.”
Galatians 6:18 — “The grace of our Lord Jesus Christ be with your spirit, brethren. Amen.”
Philippians 4:23 — “The grace of our Lord Jesus Christ be with your spirit. Amen.“
Luke 4:16 — “He came to Nazareth, where he had grown up, and went according to his custom into the synagogue on the sabbath day. He stood up to read and was handed a scroll of the prophet Isaiah. He unrolled the scroll and found the passage where it was written:
“‘The Spirit of the Lord is upon me, because he has anointed me to bring glad tidings to the poor. He has sent me to proclaim liberty to captives and recovery of sight to the blind, to let the oppressed go free, and to proclaim a year acceptable to the Lord.’
“Rolling up the scroll, he handed it back to the attendant and sat down, and the eyes of all in the synagogue looked intently at him. He said to them, “Today this scripture passage is fulfilled in your hearing.”“
The priest, by the salutation ["Dominus vobiscum"], wishes every grace to the people that the presence of God brings; and the people by their “et cum spiritu tuo“, implore that the soul of the priest be filled with God, thus enabling him to offer worthily the Holy Sacrifice.
— The Sacrifice of the Mass, M. Gavin, S.J.
Bishops can say “Peace be with you” at Mass instead of “The Lord be with you”, because that was the Lord’s greeting, and bishops are direct descendants in discipleship from the Twelve Apostles.
If the Holy Spirit were not in this your common father and teacher, you would not, recently, when he ascended this holy chair [the bishop's seat, as the bishop got up on it] and wished you all peace, have cried out with one accord, “And with thy spirit.”
Thus you cry out to him, not only when he ascends his throne and when he speaks to you and prays for you, but also when he stands at this holy altar to offer the sacrifice. He does not touch that which lies on the altar before wishing you the grace of our Lord, and before you have replied to him, ‘And with thy spirit.‘
By this cry, you are reminded that he who stands at the altar does nothing, and that the gifts that repose thereon are not the merits of a man; but that the grace of the Holy Ghost is present and, descending on all, accomplishes this mysterious sacrifice. We indeed see a man, but God it is who acts through him. Nothing human takes place at this holy altar.
– “1st Homily for the Feast of Pentecost”, St. John Chrysostom.