Why is the theory false that counting the seconds between lightning and thunder will tell you how far away the storm is?

It is not false, but it may be inaccurate, because

-- lightning can come from different parts of the storm, and hit miles away

-- if multiple flashes occur, the sound cannot be assigned to one bolt

-- the storm is high in the air, so part of the distance measured may be altitude

All the counting seconds measures is the distance between you and the closest point on the lightning's path (every 5 seconds is about a mile, every 3 seconds is about a kilometer). But sometimes warm air will refract sound away from you.