Father Austin J. Milner, O.P. offers a very fine explanation of the reasoning behind the change. The short answer is:
“And with your spirit” is the literal translation of et cum spiritu tuo, which itself is a literal translation from the Greek. This phrase, whether in Greek or in Latin, was quite strange to the ancient world. It appears only in Christian writings. It already forms part of greetings at the end of some of the Pauline Epistles: “The grace of our Lord Jesus Christ be with your spirit brethren. Amen” (Gal 6:18; cf Phil 4:23; Philemon 25); “The Lord be with your spirit. Grace be with you” (2 Tim 4:22).His full answer is well worth a read.