Him continuing would be the worst thing for him as a manager and the worst thing for Barca as a team.
He looks an absolute mess on the sidelines completely losing his composure and temper. He's too emotionally invested in his team and lacks any sense of reality or accountability. This significantly affects his ability to manage games with composure and tactics.
This is the last thing a club full of young players needs.
Xavi needs to go after the clasico. Lose the clasico (most likely event), step down and be gone. Let a new manager come and manage for the rest of the season to give them more time to prepare for next season.