Problem is that while he built up his managerial career, he was doing reasonably well with Valencia, and ultimately Sevilla with three Europa Leagues in a row. That took some doing, no doubt. But at the same time, they did terribly in the Champions League to have to drop down into the 2nd tier competition. He then went on to manage PSG, which I class in the same category as Barcelona, Man City, Bayern - teams which can still win the league with your uncle Frank in charge. Winning Ligue 1 really isn't anything to brag about when you're playing some of the best players in Europe against farmers, anyway (and for any evidence of his teams' inability to defend a lead, remember he was in charge when Barca won 6-5 on aggregate after being 4-0 down in the first leg).
So, his slightly inflated CV aside, was he the right choice as manager? Not just as manager, but as the man to replace Wenger? Probably not. We needed a big, no-nonsense personality to come in, and we got someone who after a year and a bit still doesn't know which formation he prefers (we were 3-4-3 last night).
Is he a bad manager? Also no (again, see his work pre-PSG. 3 Europa Leagues, while indicating a crap CL run, is still some achievement). He took us 22 games unbeaten after we lost our opening 2 last season, and everyone was singing his praises. We were comfortably in 3rd, a massive achievement for his first season in charge. And then the wheels came off, and we missed out on CL qualification by a point. And then got destroyed in the final of the Europa League by Chelsea, after we dominated every team along the way. And now we've extended that run into this new season.
So, what happens now? Because our next game is Leicester away, and I'm sure we all know what's going to happen. If we sack him, do we go back to our original shortlist? Was that an actual list, or was it just something the media threw together? There were still a lot of unproven names on it, and some mid-table regulars (one of whom has catapulted Leicester into 3rd, mind you). For a club like Arsenal, we need to go for a VERY big name. I'm talking Klopp, Guardiola calibre - not them specifically, obviously, but that level.