Text: I Tim 5:1-2
1 REBUKE not an elder, but intreat him as a father; and the younger men as brethren;
2 The elder women as mothers; the younger as sisters, with all purity.
Some theologians & scholars (post-Bower, Ehrman , Brown et. al.) argue that Paul can not possibly be the author of I & II Timothy or Titus since all these "Pastoral Epistles" mention "elders." They attribute these works to a later period & label the author as "DeuteroPaul" ie "Second Paul."
The argument goes that the New Testament churches were Spirit-driven anarchistic entities that did not use elders. Later, post-Clement of Rome & onward, a more monarchical, authoritarian structure developed. Therefore, these three letters must be from that later period, not from Paul. The problem with this argument is that it begs the question ie it assumes its answer in its premise. It is invalid to use the New Testament as evidence of a theory then use that same theory to invalidate part of the New Testament! Doing so makes the argument invalidate its own proof!
Other weak argument has been offered in the form of vocabulary analysis observing that "Paul" uses different words than he does in his other letters. This is very weak because, as Paul is addressing very different issues in Romans, Corinthians, etc. than he is in these three letters. By way of example, if you were writing a letter to the editor about prostitution downtown, you would use very different vocabulary from when you write your little brother or sister about getting their first job (unless of course, it is as a prostitute!). This is very parallel to Paul's situation: the other epistles are for a general audience; these are personal. The others address problems to be corrected in society or in the church; these are to exhort individuals. The list of differences continues & greatly weakens this argument, too.
All in all, the arguments for "DeuteroPaul" are very, very weak & can probably be ignored as generated by an a priori agenda that does not include honestly evaluating the integrity of the New Testament. Up against 2000 years of textual pedigree, style examination, contemporary correspondence & many other tests by which we can analyze these letters, the "Second Paul" arguments are less than second rate.