One thing i really don't like about him is he looks way too casual out on the field. I know that's his style, but it feels like he is careless. Maybe it's the French way, but it really pisses me off at times. As a fan you want to see players on the field being serious and have a fighting spirit for your team. Good examples of this are Araujo and Mingueza, who you can tell are busting their asses to make a clearance or to track down an attacker.
With griezmann it never feels like he gives a shit if he messes up a pass, shot, or a touch. He even laughs at it sometimes. I just don't like that. our previous captains like Puyol or Xavi would definitely not allow that.