Who is authorized to baptize? Can any one do it? There are two questions that the bible never directly addressed except through indirect commandments and biblical examples.
Jesus did not baptize, but rather his disciples did (John 4:1-2). Paul did not baptize many, he left it for others (1 Corinthians 1:14-16). Peter did not baptize Cornelius’s household. Instead, he simply ordered that they should be baptized (Acts 10:47-48). The Twelve almost certainly called upon the 120 for the baptism of at Pentecost (Acts 1:15, 2:41).
Who baptized Paul? Ananias? The scripture simply says “he was baptized.” In fact, this is true for most of the baptism narratives of the Bible; someone proclaimed the gospel and “those who believed were baptized.”
Paul warned the Corinthian Christians against over-exalting certain leaders and positions. He recognized that baptizing too many could lead to this, and wrote that he was glad that he had not baptized any of them, except Gaius and Crispus. Paul also baptized the household of Stephanas, another possible allusion to on-location baptism.
There are no biblical examples of new testament women baptizing anyone. There is no biblical example of sinners baptizing anyone. Jesus commissioned his apostles to go into all the world “Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all things that I have commanded you” (Matt 28:19,20).
Some with human reasoning will ask, “What if there are no Christians around, can a sinner baptize another sinner?” The answer is very simple: At what time did all Christians disappear from this planet? Since the time of Christ and His apostles, there have been Christians roaming this planet. Sinners don’t have the authority to preach the Word, nor do they have the authority to baptize anyone. Christians don’t simply baptize someone, but by the authority of the Father, Son, and Holy spirit. How can they call upon the godhead when God doesn’t know them? (Matt 7:23) Asking a sinner to baptize you would be the equivalent of asking a sinner to pray for you. Why even bother, because the scripture instructs us that a sinner’s prayer goes unheard (Jn 9:31 f; 1 Pet 3:12).
The same theory is asked if there were no Christian men, could Christian women baptize someone? First of all, when has there been a time when there were no Christian men? Secondly, women are not allowed to teach or usurp authority over men (1 Tim 2:12). Even if there were no Christian men nearby to baptize someone, women are not allowed to usurp the authority over any man, including a confessed believer who desires to be baptized.
Conclusion: If we are to abide by the authority of the scriptures, then the bible makes it very clear that only Christian men have the authority to baptize someone.