So much of the offense runs through the QB. They're reading the D at the line of scrimmage, checking out of plays and into others, and touching the ball on every offensive snap.
If a team's QB can't throw, the opposing defense doesn't need to respect the pass, can play closer to the line of scrimmage, can commit more players to run defense, and can completely shut the offense down.
If a team's QB can't read a defense at the line of scrimmage and check into the right play, the defense is advantaged—their sideline can signal schemes that are optimal based on formation, down and distance and put the offense at a distinct disadvantage.