Bishop Bernard Fellay gave an extensive interview this past November to DICI (the official news organ of the SSPX).
One central theme - the Council - Bishop Fellay addresses as follows:
... We have gone from one pontificate to another, and the Church’s situation has stayed the same. The basic lines remain the same. On the surface there are variations: one might say that these are variations on a well-known theme! The basic assertions: we find them, for example, about the Council. The Council is a reinterpretation of the Gospel in light of contemporary or modern civilization—the pope has used both terms.
I think that we should begin by very seriously asking for a definition of what contemporary, modern civilization is. For us and for average mortals, it is quite simply the rejection of God; it is “the death of God”. It is Nietzsche, it is the Frankfurt School, it is an almost universal rebellion against God. We see this almost everywhere. We see it in the case of the European Union which in its Constitution refuses to acknowledge its Christian roots. We see it in everything that the media propagate, in literature, philosophy, art: everything tends toward nihilism, to the affirmation of man without God, and even in rebellion against God.
Then how can we reread the Gospel in that light? It is quite simply not possible; that is squaring the circle! We agree with the definition just given and from it we draw consequences that are radically different from those of Pope Francis, who goes so far as to show, to expose the continuation of his thought by saying: “Look at the fine fruits, the marvelous fruits of the Council: look at the liturgical reform!” Obviously that sends a chill down our spine! Since the liturgical reform was described by his immediate predecessor as the cause of the crisis of the Church, it is difficult to see and to understand how all of a sudden it should be described as one of the finest fruits of the Council! It certainly is a fruit of the Council, but if this is a fine fruit, then what is beautiful and good or bad? It makes your head spin!