Thinking Faith have just published what I think is the best consideration that I have seen of the significance of the phrase "And with your spirit". I do not think there was much confusion about it among the ordinary faithful, as the lead paragraph of the article at Thinking Faith suggests. I found Fr Mahoney's account of the patristic and historical background to the suggestion that the phrase in some way relates to the grace of ordination of the celebrating priest very useful. I share with him the view that this interpretation seems fanciful and contrived.
It seems to me fundamentally correct to see the dialogue "The Lord be with you" /"And with your spirit" as being a greeting and a response to that greeting. This is the simple straightforward sense of how this dialogue occurs in the Liturgy, particularly at the beginning of the Eucharistic celebration. It has the nature of a greeting exchanged between the priest and the people.
Taken over into the Eucharist to express the people’s response to the celebrant’s greeting of, ‘The Lord be with you’, the phrase is to be understood fully as ‘And the Lord be with your spirit’.It also seems to me correct to take the Scriptural origins of the phrase in a literal way, looking at how it occurs in the writings of St Paul. This does not, however, mean that we should underestimate its theological complexity. The account given by Fr Mahoney of St Paul's anthropology of body, spirit and soul is therefore, in my view, the correct way to explain the response and the one that is taken in the resource Become One Body One Spirit in Christ. I would want to add, perhaps, the suggestion that in writing of the "spirit" St Paul also refers to that in man which represents his orientation or openess towards God.
In passing, Fr Mahoney suggests that the debate about how the phrase "And with your spirit" is understood is a debate about whether the priest is seen as being separate from the people or as being one with them.
I wonder also if part of the modern popularity of this interpretation in terms of the grace of priestly ordination is because it can help to propagate the difference between priests and people which the Vatican Council tried so much to diminish and which others are now regrettably attempting to re-establish.The reference to n.9 of the Decree on the Life and Ministry of Priests, where the community of life of the priest with the lay faithful is described, is quite apposite in giving a context to the greeting dialogue understood precisely as one of mutual greeting. I would not agree that, in this passage, Vatican II was making an effort to diminish the difference between priests and people, as this passage needs to be read alongside others in the Decree which discuss those particular gifts and office that a priest receives through ordination, and which do mark him out as different from the people. The relationship between priests and people as described in n.9 is one that should be our goal; but I do not think that it is reversed by a rightful consideration of the specific dignity of the priestly vocation through such initiatives as the Year for Priests.