CLAIM: Roman Catholic apologists argue that Judas’ replacement by Matthias supports the notion of papal succession. That is, instead of having a first century apostleship, this is carried on from generation to generation. Catholic apologist David Currie writes,
This is presupposed in what the apostles did in Acts 1. The fact that there was no discussion of the matter so soon after Jesus had been teaching them lends credence to the Catholic position. Christ himself must have provided for succession when he taught the apostles during the time between his Resurrection and his Ascension.
Is the replacement of Judas support of papal succession?
RESPONSE: We have already written on the topic of papal succession (see “Papal Succession”). Additionally, we do not believe that this passage supports this doctrine for a number of reasons:
First, this is not an explicit teaching on papal succession. At best, this is a biblical example—not a biblical teaching. Why don’t we have Jesus’ explicit teaching on papal succession, rather than just an assumption like this? Would God really leave such an important teaching to the level of a biblical example?
Second, the one who was replaced (Judas) was never really a believer. Judas was never a believer (Jn. 6:70; 17:12). This doesn’t fit with the Roman Catholic doctrine of papal succession, which states that a believing pope is replaced by another believing pope.
Third, in the Roman Catholic system, there is one pope—not twelve. For this passage to fit with papal succession, it would need to be Peter who was replaced—not Judas. Or we would need to have 12 popes in the Roman Catholic Church today.
Fourth, later, when other apostles were killed, there was no motion to replace them. For example, James of Zebedee is never replaced after his death (Acts 12:2).
 Currie, David B. Born Fundamentalist, Born Again Catholic. San Francisco [Calif.: Ignatius, 1996. 66.