There is a time for a mental health day and a time to push through the pain
I don't think Biles is a villain. She is, by every measure, the GOAT in gymnastics. Her record of dominance is way out in front.
I do think, as we teach children, there is another concept at play--and that is to know when to push which "key." We teach kids about doing hard things--I tought my son this, my scouts this, my YM this. I stand by it. There are times you suck it up and keep going, despite pain/discomfort. You don't give up. And you get stronger and develop more confidence.
We also do need to teach children that there are times to take care of yourself. In HS there were a few times my son was so stressed out with school that my wife told him to stay home and "reset." I learned this was wise on occasion--he needed some down time to think, sleep, etc. A mini vacation to "sharpen the saw."
However, timing is everything. You don't lay off the gas during an A.P. test, a big deadline at work, the NBA playoffs, or the freaking olympics. Those are times when you dig deep, knowing that they'll be over soon. But mental health is real and the better we all get at managing it, the more effective we perform in the long run.
I could be completely off, but I'd say the failure for Biles is not that she had a mental health episode, but the timing of how she dealt with it. If anxiety, focus, mental exhaustion, or some other issue was starting to emerge, she needed to deal with this proactively up front and not during the two-hour window when her peak performance is required. And she needed to be trained and prepared to handle this during the peak moments--to fight through.
Just some thoughts/opinions. I think what happened yesterday is a failure by her and coaches. But she certainly isn't a failure--GOAT and not even close.