Arsenal does not play possession football anymore. We used to, but that stopped 3 years ago.
We play attacking football now. Obviously we keep the ball more than most teams, but we play a pass and move brand of football and quickly make chances, not passing it around the midfield for the purpose of keeping the ball.
We play exciting, attacking football. Not boring possession football, which i judge to be more defensive than attacking.
I think I've said it already, but possession football is the most attacking football. One passing error in the build-up to a shot can result in an easy counterattack for the opponent because of how open the possession team is, with everyone in attacking positions. It's not attacking in the same sense of Reading lugging it into the box or Chelsea shooting from the half way line, it's proactive attacking. It depends how you look at it. It's defensive in the sense that you constantly attack to defend.
And Arsenal do still play a possession game, they're just not as good at it compared to 3 years a go. In my opinion, they're a more defensive team now. Without the ball, they sit deep in two banks of 4 & wait.
You don't think Valencia and Bilbao are possession teams? Bayern are better at it than Arsenal too
Unfortunately, I don't think Valencia will see as possession under Pellegrino, although saying that, they wern't particularly possession based under Emery.
All of Marcelo Bielsa's sides have been possession based & Bilbao definitely try but it's easier said than done. They averaged 57% last season, so I'd put them in the bracket of a practising possession side.