Acts 1:15-26 - the first thing Peter does after Jesus ascends into heaven is implement apostolic succession. Matthias is ordained with full apostolic authority. Only the Catholic Church can demonstrate an unbroken apostolic lineage to the apostles in union with Peter through the sacrament of ordination and thereby claim to teach with Christ's own authority.
Three quick points:
i) If you compare this tendentious summary with what Acts 1:15-26 actually says, the Catholic apologist is clearly getting out of the text what he is putting into the text. Stuffing the ballot box.
ii) It’s noteworthy that Matthias disappears without a trace.
iii) But let’s assume for the sake of argument that choosing Matthias is the exemplar of apostolic succession. Compare Acts 1:15-26 with Universi Dominici Gregis (subsequently amended by Benedict XVI) and ask yourself if the rules for papal election match the alleged exemplar:
If the case of Matthias is the yardstick, then papal elections don’t measure up.