I'm not sure it's correct to say that a 12 year-old boy has more authority in the LDS church than his mother. What type of authority? The authority to do what?
What things does a deacon have the authority to do that his mother does not? Pass the sacrament and collect fast offerings.
Am I missing anything?
But he probably does not have the authority to do other things that his mother might have the authority to do, like preside over and conduct a Relief Society meeting.
All authority in the LDS church is delegated by someone else, from the authority that the apostles have to speak in General Conference to the authority that a woman has to perform washings and anointings on other women in the temple to the authority that the deacon has to pass the Sacrament to the authority that the non-member who's visiting the ward has to also pass the Sacrament on to the next person in the pew. It's all delegated authority, and Mormons would say that it comes from God to the prophet and goes from there.
There are areas where the church has designated that the mother is most definitively in authority over her son. The church has been pretty specific that the husband is ideally meant to "preside" in the home, not the wife (though Mormons seem to be in the midst of an identity crisis as to what the hell "preside" even means). But what happens in the case of single mother households or a household where the husband is otherwise unable or unworthy of presiding?
In those cases, the church has designated that it's the mother who presides, not her minor sons. The authority goes from husband to wife, not husband to son. Dallin Oaks grew up in a single-mother household and has talked about this on several occasions.
For me, the problem is not that a 12 year-old boy has authority and responsibilities that his mother does not have. One can make the case that they have authority and responsibilities in different things, that their roles are "separate but equal."
The problem is that the 12 year-old boy is only going to grow in sacerdotal authority and responsibilities, and the mother will not. For every type of "authority" in the church that a woman is given, for every task that she may perform, men have a comparable equivalent. This is not the case with women in the church, where we can create a long list of male-only roles for which there are no female equivalents. This is why you see so many people desperately reaching for pregnancy, lactation, childbirth and motherhood as some kind of equivalent.
The boy will eventually be able to perform baptisms, give blessings, preside over Elders Quorums, and serve in any number of callings for which there are no female equivalents. The mother will always just have the limited roles that she has. That is the problem.