I'm having trouble understanding what the equation is intended to do.

=$B2:$C2=FALSE

Just fiddling with it, it seems to conditionally format if, and only if, Column B is FALSE.

At any rate, the equation will expand if you insert a column between B and C rather than to the right of C.

Also, since you are only formatting A, I don't believe the dollar signs ($) are necessary though they should not affect the calculation. (Don't take my word on it.)