As someone who suffers from mental health issues and 2 children who also have issues, no, YANBU at all.
If you haven't experienced it, you don't get it and there are a LOT of people on this thread making scathing comments because they just DON'T GET IT. But I dare say they won't be told.
They are the same folks who will be bewildered when their children develop problems, either at school or Uni and will have no idea what went wrong.
Yes, children have lots of holiday but as they get older, the academic pressure can be unbearable and children crack more easily than you may think: factor in any other health problems, problems at home (your kids DO notice if you're not getting on with your partner or are having problems at work) or sustained bullying and you would be surprised how quickly they go downhill.
I don't factor days in as such but I keep my eye on them and pull them if necessary and truthfully it won't be more than 2 days a year.
I just say something like "you're looking a bit run down, are you ok?"
If they're not ok, they will normally say they have a headache or tummy ache (often they don't know what's wrong and just offer one of those as a suitable excuse) and I give them the benefit of the doubt and a duvet day.... your children can only abuse this if you're not on the ball and that's not an issue in my house.
Are the aware they have leeway? No.
Do they know they can tell me if they're feeling "off"?
Absolutely.
Some of you need to educate yourselves... mental health problems increasing and you wouldn't send a child to school with a high temp/vomiting so why would you send your child if they were having a crisis?