The thing is that many hosts disagree with Airbnb, and see every human regardless of age as a guest. The only way around it is not to allow small children at all. Charging cash on check in is an absolute no.
So if you want to stay there, have them bill you via Air (not hard to do). Or stay somewhere else that welcomes children for free!
Airbnb didn't use to have this free child policy, so hosts may have joined prior. Then it changed, and hosts felt it unfair as small children are also generating rubbish, using linen and hot water, creating mess (more than an adult usually) etc.