The mention of "Peter's wife's mother" proves that Peter was married. His wife was likely still living, as Paul later asks in I Corinthians 9:5, "Do we have no right to take along a believing wife, as do also the other apostles, the brothers of the Lord, and Cephas?" This indicates that several of the apostles were married during their ministries.
Erroneously, Roman Catholics claim Peter to be the rock on which the church was built, the vicar of Christ, and the first Pope. How can they maintain, then, that it is wrong for "priests" to marry? If this were a sin, why did Christ not immediately reject Peter as an apostle, since he had a wife? It seems incredible that the Catholic Church would teach that Peter was its "first Pope," a model to all his successors, yet forbid its priests to marry despite his being a married man!
Priestly celibacy is specifically contrary to New Testament teaching (I Timothy 4:1, 3). Paul instructs, "A bishop then must be blameless, the husband of one wife, . . . one who rules his own house well, having his children in submission with all reverence (for if a man does not know how to rule his own house, how will he take care of the church of God?)" (I Timothy 3:2, 4-5). Scripture makes no objection to God's ministers having a wife. As Hebrews 13:4 declares, "Marriage is honorable among all."