This is such a tired argument. YouTube is ubiquitous - it is the primary (read: effectively only) platform for video hosting, which today comprises a large proportion of all information transfer between humans. Companies like Facebook and YouTube are central to social discourse, at least in the west. When a medium of communication is that ubiquitous, the fact that it is owned by a private company is not an excuse to throw up one's hands and say "Well, I guess they own it - they can censor what they want".
The fact that it is so widely used and owns such a significant share of the "ways to spread information" market outweighs the fact that the company is private.