Jamieson, Fausset and Brown on Hebrews 12:10

10. Showing wherein the chastisement of our heavenly Father is preferable to that of earthly fathers.

for a few days--that is, with a view to our well-being in the few days of our earthly life: so the Greek.

after their own pleasure--Greek, "according to what seemed fit to themselves." Their rule of chastening is what may seem fit to their own often erring judgment, temper, or caprice. The two defects of human education are: (1) the prevalence in it of a view to the interests of our short earthly term of days; (2) the absence in parents of the unerring wisdom of our heavenly Father. "They err much at one time in severity, at another in indulgence [1Sa 3:13; Ep 6:4], and do not so much chasten as THINK they chasten" [Bengel].

that we might be partakers of his holiness--becoming holy as He is holy (Joh 15:2). To become holy like God is tantamount to being educated for passing eternity with God (He 12:14; 2Pe 1:4). So this "partaking of God's holiness" stands in contrast to the "few days" of this life, with a view to which earthly fathers generally educate their sons.