Flowering into womanhood sounds so lovely, but as women know, it's not all that wonderful. First of all, there's that monthly thing, which is so looked forward to. Pretty soon that thrill wears off, and the next 40+ years seems like extreme overkill in the name of fertility. All cultures have their ritual observances of this event in a girl's life, usually emphasizing the idea that she is now looking forward to using all that fertility.
Coming out in society meant that a young lady was available to meet eligible men and hopefully marry one of them. Usually, girls were at least 16. In Pride and Prejudice, the erratic Mrs. Bennett ignored that aspect, and considered all her girls introduced into society, mainly because she couldn't see leaving the younger girls at home while the older ones went to dances and parties. Of course, everyone thought she was completely irrational, and they were right.