What is the basis for arguing that Paul should have been selected as the 12th apostle instead of Matthias?

Commentators on the story of [Acts 1:15–26](https://www.biblegateway.com/passage/?search=Acts+1%3A15-26&version=ESV) , where the Apostles select Matthias to replace Judas as the 12th apostle, often say vague things like: > Some have held that the choice of Matthias was unauthorized and that he was never accepted as an apostle. ([*People's New Testament*](http://www.ccel.org/ccel/johnson_bw/pnt.pnt0501.html)) There seems to be some biblical evidence that Paul *was not* considered (not even by himself) to be "one of the twelve," like [Acts 2:14](https://www.biblegateway.com/passage/?search=Acts+2%3A14&version=ESV) and [1 Corinthians 15:5–9](https://www.biblegateway.com/passage/?search=1+corinthians+15%3A5-9&version=ESV) . But some apparently either disagree with this assessment, or think that if Paul was not considered the 12th apostle, he should have been. So, my question. What are the arguments used by theologians who believe that the apostles erred in selecting Matthias to be the 12th apostle instead of Paul? Related: [Who was the 12th Apostle - Matthias or Paul?](https://christianity.stackexchange.com/q/7507/21576) Unlike this closed question, my question focuses on one side of the debate.