Hebrews 12:10 For they verily for a few days chastened [us] after their own pleasure; but he for [our] profit, that [we] might be partakers of his holiness.

Why are the children of God chastened? It is for their profit, so that they "might be partakers" of His Holiness.
It is important to note that only those who are chastened can be partakers. The "bastards", who are not chastened, are not capable of being partakers.

Remember from verses 6-8, that the "bastards" are unregenerate, and only the regenerate are chastened. There is no "Free Will" where the grace of election and regeneration are concerned. However, where faith and works are concerned, it is all about "Free Will".

I wish people would pay close attention to key words within certain passages, and especially the absence of key words in others.

We are received and chastened, so that we "might" be partakers.

We are buried into death with Christ, so that we "might" be raised to life.

We are delivered to Chirst, so that we "might" come to Christ.

We are given a new man, so that we "might" put on that new man.

Related passages:
1 Corinthains 12:7
Deuteronomy 8:5