I've already tried to learn various things on my own by watching videos and pretty much all of them went badly at first, so I'll admit I'm biased toward lessons. With skiing specifically the risk is bigger because you can develop bad technique habits that are hard to correct later, and then it gets frustrating when you realize you've been doing everything wrong.
Plus, there's one thing nobody really talks about much: falling wrong on skis actually hurts, and an instructor will teach you the correct arm and leg position to minimize the impact. On your own you'd figure it out the hard way, literally.