Why, that too is an arbitrary point in time. There’s no such term of art as “emotional maturity”, obviously it can mean a lot of things to a lot of people. Your emotional maturity with regards to consent is measured legally by mental capacity, but generally it's used as a measure for our most mature citizens. IQ is what measures mental capacity, though an argument can be made for the “biology of G” as a fair measure as well. Barring arbitrary age constraints, generally legal functioning mental capacity to live on ones own is minimally an IQ of 70. 25% of the population is between 70 and 90 IQ with 9% between 80 and 70 IQ.
A case can be made that if a child has an equivalent adult IQ above 70, and many do below the point of puberty, then there is no reason to deny equal rights as those given to equal mental capacities. Why is the 73 IQ marginally mentally handicapped 25 year old who is allowed to live on their own any better equipped to make discretionary decisions than the 10 year old who has an adult equivalent IQ of 90?
The slippery slope comes from the justification of homosexual unions; the same case can be made for incest, bestiality and pedophilia (w/adult equivalent capacity). The only justification for the special status of marriage is for procreation, survival of the species. Deference is given for the “possibility” of reproduction, obviously the only thing those who practice perversion can reproduce are dirt babies.