Paul is affirming that his apostleship does not have a human origin, likely in response to claims that it did.1 He is not an apostle because he was appointed such by a group of men (e.g. the Antioch church council, cf. Acts 13:1–2). He is not an apostle because he was appointed by an individual (e.g. Barnabas, cf. Acts 11:25–26; Ananias, cf. Acts 22:15).2
1 Paul, an apostle not from men nor through man, but through Jesus Christ and God the Father, who raised him from the dead