I am unconvinced that Paul wrote any of his letters.
But what on earth does he mean?
Starting from 48:40, McKnight explains that the conventional approach in scholarship to the authorship of Paul’s letters is to assume that Paul certainly did write some of his letters (such as Romans and Philemon), and then to compare the style and vocabulary with the more disputed letters (such as Colossians).
The problem with this is that Paul clearly didn’t write even some of his ‘undisputed’ letters! For example, in Philemon 19, we read:
I, Paul, am writing this with my own hand.
Similar things may be found elsewhere in the ‘undisputed’ letters (such as 1 Corinthians 16:21). The implication is that Paul didn’t write the rest of the letter in question.
The suggestion favoured by McKnight is that Paul would have drafted his letters in conversation with one or more of his companions, such as Timothy. This ‘committee’ would have consisted of different people at different times and in different places, and would have resulted in letters that differ in style from each other. This is different from suggesting that Paul dictated his letters, or from suggesting that Paul used an ‘amanuensis’ to draft his letters on his behalf. The work of E. Randolph Richards was mentioned in this context: Paul and First-Century Letter Writing.
(Keep in mind that there’s a difference between writing a letter and being its author. If you ask me to write out a letter, and then you read it through and sign it at the bottom, I wrote the letter, but you are its author. Or, for another example, I am the umpteenth co-author on numerous scientific publications that I hadn’t even read prior to their publication!)
So, in conclusion, McKnight likes to say of Paul’s letters:
Since Paul did not write any of them, he wrote all of them. That is, I think he’s behind all the letters that bear his name, and I don’t think that he dictated or wrote any of them, but that they reflect different groups of people with whom he was ministering at the time.