Well, I don't know your situation or even whom the argument is being crafted for (Music director? Master of Ceremonies? Bishop?) but it's easy to imagine scenarios in which the change could be an improvement!

We've moved to extending a solo antiphon (American Gradual, usually) till the line is finished and starting a hymn when everyone is back within reach of a book, which usually gets opened.

Rather bizarre, I should say, that anyone other than the choirmaster is making this decision!

In Canada we have an official hymnal, that is, a hymnal edited by a commission of the Bishops' Conference, and officially approved. So any (suitable!) song from the CBW may be used at Mass at the entrance, offertory, or communion, according to the rubrics.

It's true that a song wholly ad lib is (only) allowed post-communion, but because only there does the GIRM omit the usual "from Graduals or other approved chants" condition.

It's quite correct as @StephenMatthew says that motets, anthems, spiritual airs, and what not, sung by the choir, are not allowed at or after Communion. Presumably the right place for those of appropriate is at the Offertory.

Does this help? From pages 37-38 of the CCCB National Liturgy Office's Guidelines for Liturgical Music (revised, 2015 edition):

The reception of Communion has traditionally been accompanied by the singing of a psalm with an appropriate antiphon. The texts for the Communion antiphons in the Roman Missal are intended to be sung with appointed psalm verses which are indicated in the Graduale Romanum or the Graduale Simplex. Musicians may wish to consult these books. Settings of Psalm 23 and Psalm 34 are especially recommended for the Communion procession.

Then it talks about the types of hymns that are also appropriate.

And then this practical note:

In order to facilitate the assembly’s full participation in the Communion song, it is recommended that hymns with refrains be used during the procession. The cantor or choir can sing the verses and the assembly can easily join in the refrain without having to carry a hymnal in procession.

http://nlo.cccb.ca/images/stories/pdfs/guidelines_liturgical_music.pdf

.

'another liturgical chant approved by the Conference of Bishops'

If it's not in CBW, you could seek evidence of explicit approval by CCCB (not just the diocesan authorities). Perhaps, like the Australians, there is a list of approved hymns?

Canadian GIRM:
86. While the Priest is receiving the Sacrament, the Communion Chant is begun, its
purpose being to express the spiritual union of the communicants by means of the unity of
their voices, to show gladness of heart, and to bring out more clearly the “communitarian”
character of the procession to receive the Eucharist. The singing is prolonged for as long
as the Sacrament is being administered to the faithful.74 However, if there is to be a hymn
after Communion, the Communion Chant should be ended in a timely manner.
Care should be taken that singers, too, can receive Communion with ease.
87. In the dioceses of Canada singing at Communion may be chosen from among the
following: the antiphon from the Graduale Romanum, with or without the Psalm, or the
antiphon with Psalm from the Graduale Simplex, or some other suitable liturgical chant
approved by the Conference of Bishops of Canada. This is sung either by the choir alone
or by the choir or a cantor with the people.
However, if there is no singing, the antiphon given in the Missal may be recited
either by the faithful, or by some of them, or by a reader; otherwise, it is recited by the
Priest himself after he has received Communion and before he distributes Communion to
the faithful.
88. When the distribution of Communion is over, if appropriate, the Priest and faithful
pray quietly for some time. If desired, a Psalm or other canticle of praise or a hymn may
also be sung by the whole congregation.

As to the clarity of the US GIRM: it starts by listing as option 1 the missal text which when it was introduced was explicitly said to be a spoken only text, NOT used to displace the sung text.
And it ends by delegating the authority to the bishop of the diocese, which is (mis)used, as other posts in this forum have stated, to mean that if any US diocese has an official publishing house then anything published by it has liturgical approval anywhere in the USA. It may be that USCCB has explicitly approved this, but it cuts the ground from under the feet of bishops who would prefer a better regulated liturgy.

Notwithstanding the many errors and contradictions found in these guidelines, it is so politically weighted, it borders on the embarrassing.

To address again the original query, if you are not singing any of the official options available, then whether the musical item is responsorial or not is subjective. I could never choose some modern twaddle about eating bread and drinking wine because it has a catchy refrain over something meaningfully catechetical without a refrain.

I'm not sure what point you are trying to make, but the use of anything other than the official chants is always second-best. Within that less-than-ideal scenario, whether the piece being sung is responsorial or not should be within the remit of the music director. I cannot accept, in this instance, that it follows that a piece is better because it is responsorial. Even if an episcopal conference publishes a document recommending one practice over another, outwith the official chants, it is merely that: a recommendation. Take it or leave it.
Universally, the permission is given for another suitable hymn or psalm to be sung, either as well as the prescribed chants or in place of them.
All sensible music directors will choose a piece that is fitting and worthy for the Mass as a whole, and that it is suitable for that place within the Mass. I am pleased that it is becoming more common for the prescribed communion antiphon (or another, seasonal or ad libitum option) to be sung before any other hymns/psalms. I almost always disregard hymns with refrains because they are very often trite. I think the idea of unifying the congregation through song as they process to receive communion is rather academic. Most will prefer their own private prayers and devotions. Most likely, they will sing after they have received, by way of a communal thanksgiving.
Finally, I have found that trying to tailor liturgical choices to, and try to appease, a congregation is folly. Most simply won;t care whether the hymn at communion has a chorus or not. If they like it, they will want to sing it. If they hate it, they won't bother. And the idea of choosing music so as to try, desperately, to make a congregation sing is also folly. How often is the misrepresented notion of 'full, conscious and active participation' laid on the shoulders of the music director? It is not their job to do that. It is the individual within the assembly's responsibility to actively participate fully and consciously at Mass. Within the rubrics, allow them the opportunities to participate. It's not your fault if they don't take those opportunities. And on that point - don't force them to join in with every single element of Mass. Keep it correct: Dialogues, Sanctus, Pater Noster, Psalm, Alleluia, Kyrie, Agnus Dei, Gloria, Credo, propers (more-or-less in that order) and then worry about whether they are singing hymns with refrains!
Finally, to the OP - always try support your music director and don't bother fighting them on an irrelevant, and very small, point. In St Michael's there are 100 other things to worry about than whether the communion hymn has a chorus!

To clarify, the change was not made by the choirmaster/music director but by the Cathedral rector, a known opponent to traditional music in the parish (unfortunately). The last choirmaster here was just fired for being too traditional, actually.

To clarify, this is only a hypothesis with much evidence to support. Most of these changes of which I speak, including the "no descants in Lent" the previous choirmaster would never approve.

But when the Latin IGMR says that unity of voices expresses unity of spirit (per unitatem vocum exprimere unionem spiritualem) what kind of singing is it prescribing or proscribing?

The phrase originates in a 1967 statement about liturgical singing in general, not just at communion.

The rubric blathers on at this point about joy of heart and "communitarian" spirit of the procession. The rubric literally uses scare quotes, showing that Latin is not, after all, a sure protection from wooly thinking.

It is important not to forget that parishes vary enormously in size, talent, and the resources which can be devoted to music. The Church authorities have not lost sight of this, they provide GR for parishes with the talent available, for others wanting chant they provide GS which gives psalms with antiphons. They provide, sporadically, translations of the graduals for local provision of musical settings. They give permission to sing other songs, and recommend polyphony for, again, those with the resources.

We have a Sunday congregation of around 100, four of whom are prepared to volunteer as cantors. We have an electronic organ, and a pianist (non Catholic) who tries to play it. We sing the Ordinary, just one setting, the ubiquitous Alleluia, an Offertory hymn, and one verse of an entrance hymn. For me, the best I could hope for would be the antiphons and psalms from GS, or an equivalent in English. Currently at Communion we say the Missal antiphon, and then the organist plays. It could easily be worse, I know at least two parishoners who strum guitars and sing, fortunately the pastor would not countenance that. (Also, we sing the Asperges once a month, less than one in ten of the congregation joins in audibly with the cantor.)

@Andrew Malton: I don’t think GIRM/IGMR prescribes or proscribes any particular kind of singing. The discussion of the chant’s purpose doesn’t lend a lot of support to any particular interpretation of what one “should” do, other than that I think “unity of voices” probably effectively favours communal singing (either choral or congregational) rather than solo singing.

@a_f_hawkins: Alas. Yeah, if your priest won’t sing—which I assume means he won’t want singing of the Creed or Our Father, either—that’s unfortunate.