Move the line to the off side. With the wind blowing toward the casting-arm side, keeping the line in the same plane lets the wind push it back toward the caster’s body and head. Taking the line to the other side — the off-side plane — puts it on the far side of the body from the windward arm, which is what the safety advice is asking for.

The other options make the problem worse. Adding force in the same plane only sends the line harder into the wind and does not move it away from the caster. Putting an observer directly downwind stands them where the wind is carrying the line and fly. Ignoring the back cast ignores the half of the cast that is coming back at you.

On the water, the same move buys accuracy as well as safety: cast on the side the wind allows, and keep the observer behind you and out of the line’s path. If the off-side plane is not enough, move your position rather than fight the wind.

Source

From the FFI casting lessons on off-side casting and wind management and safety; terms follow the FFI Fly Casting Definitions.