I am pretty well trained in early years etc and feel quite equipped to look after a baby or small child. Hand me a lizard or a canary or even a fish and I wouldn't have the same level of knowledge about what they need/ how to address any illnesses etc.
Also, unless there are other issues, children can eventually tell you when they are hungry/ thirsty/ cold/hot/ tired /sick/ where is sore etc, but with a pet that will always be guess work to some extent. You raise children to be independent- this works as we age - pets will always require the same level of care and input from you. Plus if you are disabled, depending on your disability, it can be easier to care for a child than to, say, walk a dog or clean out a fish tank.
I'm also not allergic to my ds thankfully.
I assume the point you are trying to make is actually about responsibility and empathy rather than the practicalities of it. And yes in that respect they overlap.