I also think there should be an option to select no under 18s (or no under 16s) if you don't want to host children.
An Airbnb Rep explained to me that they classify anyone over 12 as an 'adult' for payment purposes, i.e. charge the same as adults, but clearly a 13-year-old is a child, not an adult.
I have selected no infants and no children, but there is no option to select no children older than 12, so I get so many requests and bookings from people with kids and then have to pursuade them to cancel. Some people get upset and I recently had one guest get quite irate about it.
Of course I specify in my house rules that I don't accept under 18s, but that makes little difference as most people don't read the full listing or rules. If they have a way to book despite those rules, they will.