Parents always hold some fear for their children. In respect to a possible military career, the parents
may fear the loss of closeness with the sibling, fear of danger in a military career, fear the sibling
may not succeed and risk loosing time, money, or investment as examples. You'll likely have to
understand (or you may already) the nature of their fear.
At a more mature age, one may have more understanding of their own motivations. A military
career provides education and experience, medical/dental benefits, a solid pay structure,
incentives, good vacation, and most trades/specializations leads into civilian life quite well.
This kind of employment can't be provided through most civilian streams. There are draw-backs
to military life, but I doubt that is the heart of the matter.
Good luck.