Renting will effectively (as the video outlined) leave a surplus of money in your pockets. Which you will use to buy the latest gadgets, to pay the latest cool service, to take fancy trips around the globe, to hunt the last ever living rhino in Africa or whatever else. BUT, thinking in perspective, after 20 years you will anyway have 0 cash in your pockets AND no house. Until your health and job keep up, this might be fine. In case of need you will just be f---.
What you are really doing, when you buy a house, is forcing yourself in saving a liable equity for you and your family. Not only it will free you from any rent after 30yrs, but you'll also have a tangible good and you'll leave something for your children and relatives. Not even mentioning that, in case of extreme need, you'll be able to sell it.
Not sure how the concept of "house" might differ between Europe and the US and i realize that if you buy a really crappy built house, my arguments might not be valid. But where i live, houses are built to last centuries and they are by far the best way to responsibly spend your money.
Doing a Khanacademy video advising people in renting vs buying is just SO wrong. The video itself is not only rounding numbers in a bad way (IMHO), but it's also giving a superficial and quite-not-always-true message.
Horrible.