I think if you film enough men and ask enough questions, you'll be able to edit a video of enough men forgetting this information. The truth is, just because something is important to you, doesn't mean it is important to anyone else. In an ideal world they'd understand exactly what you want from them.
It may be possible to run a similar video experiment where you film enough women and ask them basic questions like 'what's the first car you owned?' and 'where's the fuse box in your house' or even 'how much is your total household budget'. My grandmother wouldn't have been able to answer any of those questions, my Mum would get one of the three. Other women might get all of them correct. The same is true of most men. Most men I know are well aware of their children's birthdays and their partner's birthday and many other pertinent facts.
But the editing can make it look like all men are feckless and that's the finding the answer you want before considering the question. Do you think it's necessary for a father to know his kids birthdays in order to demonstrate he loves them? What reasons might men have that mean they don't remember such a thing? Isn't it better to know where your fuse box is and how to change the oil in a car? Those things keep kids safe. Women! Always with the dereliction....
and i know what you're going to say.... 'not all women!'
eye roll.
You see the problem?