I'll admit, I knew this used to be the case in the US, but only recently realised that it was still happening, and that the "reasons" (read: excuses) were mind-boggling.
But do you want to know the real reason? (Sorry, that part of me is going to come out now.) Control. Not necessarily political control, but control (i.e. limits) of autonomy.
I'll give an Australia-centric example of what can happen. Now, marraige here is set at 18, 16 with permission. However, you could be deemed as being in a relationship by the Department of Human Services, even if you're trying to escape an abusive relationship. That means your husband can still take control of your finances, including any benefits you could be entitled to.
If you're wondering how this relates to child marraige, remember that a minor is still under guardianship, either by a parent or a legal guardian (including spouse). This means they can take control of finances, job prospects, education...