The Hans Küng drinking game, if you don't know it, consists in listening to a lecture by the Swiss theologian Hans Küng and taking a drink every time he takes a theological topic -- infallibility, the Trinity, Christology -- and makes it about himself. Actually, it should probably be kept entirely theoretical because, as you know if you have ever been subjected to watching a lecture by Hans Küng, you would get very drunk, dangerously drunk, very quickly. Theology for Hans Küng seems to have as its subject the Twelve Labors of Hans Küng. I thought of that a bit when I read Küng's recent appeal to Pope Francis on the subject of papal infallibility, which he does, indeed, make primarily a discussion of his own experiences and travails.
I find the comments section somewhat more interesting, as the readers of the National Catholic Reporter quickly end up running through pretty much every possible anti-infallibility position imaginable. Most interesting of all was that some of the commenters start arguing that the problem is not papal infallibility but magisterial infallibility -- which is actually more sensible than anything Küng himself usually argues, since the doctrine of papal infallibility is just that the Holy Spirit, as the Spirit of Truth, has an infallible authority to teach, and that the Church, insofar as it is animated by the Holy Spirit, sometimes in teaching does so out of the Holy Spirit's infallible authority to teach, and that the Pope's teaching, when he is teaching as successor of Peter and sign of the apostolic unity of the Church, is one of the ways in which the Church does so. Since the Holy Spirit necessarily has infallible teaching authority, the bulk of the doctrine rests entirely on the nature of the teaching authority of the Church. Once you grant that the Church has any kind of magisterial infallibility, the only question left with regard to papal infallibility is whether the Pope ever, in any exercise of his office, is the 'official voice' of the Church, or, to put it another way, whether the Church ever teaches in this way by way of the Pope as successor of Peter. (And if you look at the definition of the doctrine by Vatican I, you notice immediately that the primary bulk of the argument is papal primacy, the sense in which the Pope guides and speaks for the entire Church; papal infallibility is treated as nothing but a particular clarification of papal primacy, and the actual definition explicitly connects papal infallibility with ecclesial infallibility.)