I beg to differ: thirteen is the right age to start experimenting with dating as long as you don't expect to go clubbing or something like that, but going to eat an ice cream and experimenting with kissing or something like that is perfectly normal at that age.
Starting to date at the age of 16 is in my opinion a bit late because they are not prepared for the experience of people their age who are almost ready to have sex at that age.
I base myself on a sexual outing curve that I observed in myself, my friends, my friends friends and other children.
between the ages of ten and 12 sex is much debated among each other and with adults, they will laugh about anything which might be considered sexual. They will know more synonims for sex then you but when you really ask what that means you'll just get an answer like "well you know gighel gighel." Traffic light relationships are quite common (on off on off ect.)
At the age of thirteen dating begins many boyfriends a lot of holding hands and a bit of (french) kissing. Boys might look at porn out of curiosity and talk about it with their friends
And at the age of 16.9 in the US and 16.4 in the Netherlands (durex 2004) most will have sex for the first time.
a bit later sex becomes a topic which is discussed by teens as any other normal topic among their circle of friends
I think it is even essential in their upbringing though that doesn't mean a parent should sit back and relax, but as long as you as a parent knows what your son or daughter is up to it is ok for them to date.
Another important thing is to educate children about sex before they are twelve because they'll learn from their friends otherwise and that is not a good thing. And if you give sex education don't talk in don'ts and well don'ts (rebellious nature of teens remember) but more along the lines of sex is a wonderfull thing when two people love each other, it is important to acknowledge that sex is pleasurable because teens aren't stupid they know there is a multibiljon dollar porn industry and that it isn't because it isn't fun to do. Also if you make it look like an evil thing it will be even more wanted for teens because they reject authority and they know it is pleasurable.
One more note to the 13y old girl: I still think you should listen to your mother since you will need her a lot longer then any of the boys you will date. But you might engage to you're mother in an adult conversation why you can't go out (ADULT conversation because if your mother knows you can handle this subject she might be more willing to let you go. screaming doesn't work for sure.)