Why the first amendment doesn't apply to Yahoo shutting down answers or shutting down the comment section?

Yahoo shutting down answers or comments isn't a first amendment issue as some think. The problem comes down to the first amendment and thinking a companies

like Yahoo or Facebook would not have terms of services to "protect themselves" 

and in the end it doesn't matter they are a private company and can ban someone 

or remove comments at will if it draws to much negative attention. Or even google red flagging conservative sites or removing sites from the search engine during the elections to help democrats.