It's a well known problem[0][1] with accepting parental assertions around their child's health. That's why kids are often given time alone with their doctor, to express feelings they wouldn't otherwise feel comfortable about. Additionally, it's been shown that a parent is not great at objectively evaluating their child's emotional state or place in the world. [2]
It's even got an entry in TVTropes![3]
But why would you have a "sorrowful empathy" because I have a passing knowledge about childhood and children? You can't seriously think you're going to always know what your children are thinking or that they're even being entirely straightforward with you now, can you? Surely they have their own lives by now even a little bit, some space for their own that you're not involved in and don't know about.
[0] https://pubmed.ncbi.nlm.nih.gov/15473508/
[1] https://archive.nytimes.com/parenting.blogs.nytimes.com/2009...
[2] https://www.psychologytoday.com/us/articles/201407/parents-j...
[3] https://tvtropes.org/pmwiki/pmwiki.php/Main/DoesntKnowTheirO...