As arrows are in the hand of a mighty man - They are what a parent may rely on for defense in danger, or for help in securing provision for himself and family - as the warrior or the hunter relies on his arrows.
So are children of the youth - Sons in their youth; in their prime and vigor. The comparison of sons with arrows or spears is common in Arabic poetry. See Rosenmuller, Com. in loc. Also Morgenland, in loc.

As arrows are in the hand of a mighty man - Each child will, in the process of time, be a defense and support to the family, as arrows in the quiver of a skillful and strong archer; the more he has, the more enemies he may slay, and consequently the more redoubted shall he be.
Children of the youth - The children of young people are always more strong and vigorous, more healthy, and generally longer lived than those of elderly, or comparatively elderly persons. Youth is the time for marriage; I do not mean infancy or a comparative childhood, in which several fools join in marriage who are scarcely fit to leave the nursery or school. Such couples generally disagree; they cannot bear the boyish and girlish petulancies and caprices of each other; their own growth is hindered, and their offspring, (if any), have never much better than an embryo existence. On the other hand age produces only a dwarfish or rickety offspring, that seldom live to procreate; and when they do, it is only to perpetuate deformity and disease. It would be easy to assign reasons for all this; but the interpretation of Scripture will seldom admit of physiological details. It is enough that God has said, Children of the youth are strong and active, like arrows in the hands of the mighty.

As arrows [are] in the hand of a mighty man; so [are] (f) children of the youth.
(f) That is, endued with strength and virtues from God: for these are signs of God's blessings, and not the number.

As arrows are in the hand of a mighty man,.... Are shot out with great strength; come with much force, and do execution, and do not return in vain; with which men defend themselves, and annoy their enemies; see Jeremiah 50:9;
so are children of the youth: not young children, or children in their youth; but such who are born to their parents when they are in their youth; and which are generally healthful and strong, and their parents live to see them grown up; and who are useful to protect them, and defend their persons and properties from enemies when grown old and feeble, and unable to defend themselves: whereas children born to them in old age are generally unhealthy and weak; and besides, their parents rarely live to see them brought up, or to be helpful to them. So Christ's spiritual seed and offspring, who are the dew of his youth, are strong, and overcome the evil one; and are serviceable in the defence of his cause and interest.

Youth - These he prefers before other children, because they live longest with their parents, and to their comfort and support, whereas children born in old age seldom come to maturity before their parents death.