While a few of these are clearly weird batshit parents (the first tooth one made me laugh though), most just seem like normal parental pride, including the OP. Why shouldn't a parent post about child working on things online?
I assume you're sneering at "resilience" because clearly her son is too stupid to get anything else? Well, as a parent whose child has had to build resilience because it's true, he's never going to win the English, Maths or Science prize and everything is much harder for him, believe me, I've been pretty damn proud of him when the teachers tell me that his determination and resilience are impressive.
Personally, I don't put stuff like this up online, but I can easily imagine myself mentioning such things to people in passing if we're talking about the DC. Why is it not allowed to be proud?
I remember a friend from another country once telling me she finds sports day at her children's private school just so so weird. No one cheers the kids on and half the time they act like they aren't even watching. She said she is always the weird woman yelling for her children, her children's team, her children's friends, the child who's coming last but really trying etc. She can't get her head around this attitude that we shouldn't be celebrating the children's achievements, whether that's a win or just successfully completing the course.