Theophylact of Ohrid

Not only out of people-pleasing, he says, but also out of ambition do they do this. For not out of zeal for the law and not for the sake of piety, he says, do they accomplish this, but out of ambition: "that they may glory in your flesh," that is, to boast in the circumcision of your flesh, since they are supposedly your teachers and have you as disciples.

Commentary on Galatians ↗

Oecumenius

"but they desire that you be circumcised." He shows that vanity is the aim of all their actions. For he says that these who are circumcised and who circumcise you do not do this as if keeping and observing a law, but in order that they may have an occasion for boasting by circumcising you. For that is what he means by "in your flesh," namely, that they may be teachers, he says, and have you as disciples.

Commentary on Galatians ↗

Thomas Aquinas

But because the false brethren might say that they urged circumcision not for that reason, but solely because of their zeal for the Law, then excluding this, he proves his proposition thus, when he says: "For neither they themselves who are circumcised keep the law." For it is obvious that if through zeal for the Law they urged certain ones to observe the Law, they should also command the Law to be fulfilled in other matters. …

Commentary on Galatians ↗