Leaving aside for the moment the incongruity of accepting the papacies from John XXIII - Benedict XVI, but not Francis, Coffin gives these 7 pieces of evidence for his position:
Evidence items:
1) The term “pope emeritus” has no precedent and is confusing
2) Pope Benedict XVI seems to have resigned only part of the papacy, the active ministerium, not the office or munus of the papacy
3) Pope Benedict’s longtime personal secretary Archbishop Georg Gänswein has made statements that appear to affirm Benedict's continued papal identity
4) Pope Benedict's correct form of address is still “Your Holiness”
5) There are at least three errors in the official Latin “declaratio” read by Pope Benedict on February 11th 2013
6) "Universal peaceful acceptance by the Church of Francis has never really occurred
7) The canonically illegal behavior of the St. Gallen Mafia cardinals in conspiring to vote in their man from Buenos Aires in 2013 invalidates the Conclave
I haven't had chance to listen to his 30 minute video, but I would be very interested in what he has to say on point #6 (as it is a point of contention between R&R and some sedes).