> Why did Paizo use a license not designed by them?
I don't know their exact reasoning, but I always add licenses when publishing software I write, and they always are ones I didn't design (because I've never written a license myself). I don't think it's that crazy to use an established license that seems to be working well in a community you'd like to emulate when trying to launch you're own; I doubt Paizo had any more idea than the rest of us that WotC would pull something like this.
> And if they did a full rewrite, are they under any obligation at all to Wizards of the Coast? If they used the OGL to allow third-parties for Pathfinder, not D&D, what does this have to do with WotC? And cannot they simply switch to another license, if 2nd edition is truly a full rewrite?
My (admittedly primitive) understanding of licensing was that once something was released publicly with an indefinite license, it generally wouldn't be possible to retract that later. The copyright holder can change licenses as they see fit, but nobody will be bound by the new license unless they accept it or use a new version of the product that doesn't offer the old license. This leads me to theorize that one of a few things could be going on here:
1. The new version of the OGL (1.1) disallows you to continue using the old version (1.0) once you start using something with it. If this turns out to be the case, then people would be able to continue using the materials as-is at the last point where the OGL 1.0 was offered, but they wouldn't be able to use any future changes without accepting version 1.1 as a replacement for all of the preexisting content as well. WotC might have only intended this, but due to poor communications and/or wording in the license change, people got worried and then the narrative got out of control
2. The license works like I described in option 1 due to WotC knowing that they can't actually retroactively change the license for people already using it, but they intentionally obfuscated this to try to scare people into switching to using the new version even if they shouldn't technically have to
* The license does actually a say that it's overriding the previous one, which is not actually something a license is supposed to be able to. WotC either doesn't realize this or is hoping that in a legal battle they either can either prolong it to starve their opponents of resources or manage to convince a judge to rule against the existing consensus and establish a new precedent.
I think that option 2 is the most likely by a slight margin, but I might be biased as someone who played PF1 and now plays PF2. Option 3 would be the scariest to me given that a prolonged legal battle seems like it would be the most insulated from public opinion, which I think is mostly against the new license right now.