I get that as well. Traditionally, Catholic apologetics entails demonstrating the claims of the Church to be the authentic and true Church founded by Christ and a reliable guardian of Catholic doctrine. Yet we have Jorge and the problem of V2. Really, the only approach is to bluntly tell them that the Church has been infiltrated since 1958 and these men are not popes. Unfortunately Vatican II and the V2 Papal Imposters discredit the Church and the Church's claims, and in fact validate Eastern Orthodoxy and/or Old Catholicism ... if you grant that these men are real popes. That is yet another reason why SVism is the way to go.
Here's a typical problem I face:
Prot: But Francis/BXVI/JPII did/said [insert heresy/heterodoxy]...
Me: That's why we consider them anti-popes.
Prot: So each time something displeases you about a pope, you declare him an anti-pope...
I think that there are two ways of answering this:
1) Prove that there are reasons to believe that these men were never popes in the first place (BXVI known for heterodoxy since the 60s, JXXIII suspect of heresy since the 1910s, etc.)
2) Analyze their particular statement to show that it directly contradicts all previous doctrine.
The second way is tiresome and obviously I don't know all the answers nor can I cite from memory all dogmatic docuмents that are contradicted by the anti-popes. Also it could suggest that the pre VII doctrine is in some way on the same level as the post VII. "At the end of the day it's just two guys,
Pius V and Paul VI, contradicting each other!" - the prot could say.
Would the answer 1) be valid?