motivates people to get in their cars (induced demand)
increases the price you pay for housing
significant socioeconomic damage (car-dependency makes it harder to escape poverty, poverty increases crime)
In summary, the idea of the video is that cars are overall one of the worst means of transportation. "Free" parking just means someone else pays for it, instead of the direct users. So it is a subsidy, which makes even those people pay who don't use it. Which in itself is not a bad thing, if the subsidized thing is a good thing (health care, education, public transport), but in this case it is. The subsidy also makes cars seem more attractive, when we actually need to make them less attractive.