I think that the moment you start making big money from someone else's business is the moment that they get riled. That and when you really hurt their business. I suspect that the NYtimes thinks that IA is damaging them in the order of (possibly) $100k pa, and that it thinks that OpenAI is making in the order of $10M's from their content (and possibly doing some damage as well). It's an easy commercial decision to ignore one and go after the other - especially as going after IA is going to create some backlash as well.
