schoolmaster
(Greek, "paidagōgos", "child-conductor"); "among the Greeks and Romans, persons, for the most part slaves, who had it in charge to educate and give constant attendance upon boys till they came of age." -- H.A.W. Meyer.
The argument does not turn upon the extent or nature of the pedagogue's authority, but upon the fact that it wholly ceased when the "child", (Galatians 4:1), became a song of Solomon, (Song of Solomon 1:1); (Galatians 4:1-6), when the minor became an adult. The adult "son" does voluntarily that which formerly he did in fear of the pedagogue. But even if he does not, it is no longer a question between the son and the pedagogue (the law), but between the son and his Father -- God.
Compare (Hebrews 12:5-10); (1 John 2:1); (1 John 2:2).