Here's the problem, less than 12 months ago Josh and Stan decided to go big on Arteta and essentially let him run the whole operation when they promoted him to manager and have continued to back him fully since, giving him a wad of cash to spend this summer. Sacking him now would basically be an admission that they've not only fucked up by backing him at varying stages over the last twelve months, but it would also be an admission that they've just handed over £125m to a guy that isn't up to the job.
What makes it ridiculous is that Arteta now has a virtually impossible job of turning things around, he is almost certainly going to fail to live up to the insurmountable task he's set himself up for, so we're all just playing a game for the sake of optics, pride and stubbornness.