John Chrysostom

Having warned them therefore against this grievous pest, and amended them, He instructs also how they may escape it; by humility. Wherefore He adds also, "He that is greatest among you shall be your servant. For whosoever shall exalt himself shall be abased, and whosoever shall abase himself shall be exalted." For nothing is equal to the practice of modesty, wherefore He is continually reminding them of this virtue, both when He brought the children into the midst, and now. …

Homily on the Gospel of Matthew 72 ↗

Theophylact of Ohrid

Showing them what is to be gained by humility, He says that he who is great among you should be your servant and the least.

Commentary on Matthew ↗

Thomas Aquinas

He that is the greatest among you shall be your servant. After he has drawn them back from pride, he exhorts them to humility. And first he sets forth the exhortation; secondly, he assigns the reason. And this can be continued as follows. Chrysostom says: you ought not to be called fathers, nor masters; hence you should not seek these things ambitiously, but rather humility. Hence, he that is the greatest among you shall be your servant, i.e., he ought to show himself a servant. …

Commentary on Matthew ↗