If Newton's third law is correct, why are walls not indestructible? In applying a force to a wall, if it breaks surely it is not giving an equal and opposite force.

It is best to consider this in slow motion. First we have a wall which is at equilibrium (no external forces/all forces are balanced). Someone decides that the wall is in its way and wants to break down the wall with a wrecking ball. As the ball first makes contact with the wall, the molecules and atoms that make up the wall are pushed together in some areas and apart in others. Because these atoms and molecules are bonded together, this creates additional forces on those bonds. At this stage, the wall is still providing an equal an opposite force on the wrecking ball, as it is not falling down. As the wrecking ball moves further into the wall, the internal forces increase. Eventually, the bonds will be unable to withstand these forces, and start to break. Each time a bond breaks, the reaction force on the wrecking ball is decreased, but so is the force on the wall, because it is able to move with the wrecking ball. Eventually, enough bonds break that the wall falls down, and the wrecking ball continues it's motion. However, it's motion will be slower than before it hit the wall, because the heroic wall has enacted a force on the ball. The force on the wall (and therefore on the ball) is never greater than the force required to break the wall.