The reason that they say that seems to come from two or three rather simple sources. The first source, I think, comes from the part of the parent's mind that says "Cheer up!! These are the best years of your life!!"; this, of course, means that either the parent has made a myth of his or her own past in which he or she lived a trouble-free existence free of the bullying, fears, hectoring, confusion and snobbery that actually filled his or her days. This seems to be a lot of the problem with John and Elly because they spent their days amongst what looked to them like care-free children without ever quite troubling themselves to admit that Mike, Liz and April suffered from the same sort of insane fears and counter-productive misapprehensions that they themselves escaped from.
This leads us to the second source of the belief. Simply put, the belief that all of childhood's woes came to an end for everyone forever when they hit twenty and thus must never be considered because it would be a waste of time causes John and Elly to envy their children the contentment they foolishly presume exists. Said envy leads to anger when they encounter evidence that the evils of childhood have not gone away merely because they're no longer children. Since they're simpletons, a cry for help is transmuted into an act of defiance because it contradicts their need to live in denial.
Even if we can get past those two hurdles (which they did when they celebrated 'Elizabeth Day'), we have to clear the ultimate obstacle: the fact that there isn't one on the calendar yet. Given the intense literal-mindedness of the two drips, they must assume that since 'they' didn't create a Kid's Day, it was for a reason.