Everyone knows a major goal of parenting is that children end up independent. TCS wants to have that goal in mind from the very start. In general, TCS is disposed to consider it good when people have control over their own lives.
Conventional parents think the way to make a child independent is to decide what the components of a person ready for independence are, make a list, and then instill each item on the list into the child, no matter what he thinks of them.
Conventional parents all defend this attitude, and everyones' right to parent this way, even though their lists of what makes a person ready for independence are very different. They disagree about what parents should do, but agree that each parent should decide for himself what's needed and do that.
This is indefensible to Popperians. We know that errors need finding and correcting, and devising a master plan, way in advance, and ignoring the child's ideas, is a recipe for mistakes not to get found or fixed. People will reply saying they do listen to their children, and take into account that feedback, and then make a final and fair decision themselves.
What's the difference between not listening to someone, and listening only to the parts you find agreeable? If the issue is changing your mind and finding ways you are mistaken, then there's no difference at all. Taking under advisement only the stuff you find reasonable is a recipe for not finding out about any of your mistakes. It will catch the very easy mistakes, like if someone points out you made a typo you'll fix it and thank them. But the hard mistakes to correct are the ones where you have a blindness, and don't see that you're wrong. In those cases, anything that contradicts you seems unreasonable, so only listening to "reasonable" stuff means never fixing those mistakes.