"Johnson" generally argues like this:

Assume X is a good reason for why God allows there to be evil. If X, then Y. [There is usually some additional layer of argumentation to get to this premise.]

But not Y.

Therefore, by reductio ad absurdum, X is not a good reason for why God allows there to be evil.

Example:

X = It is best for us to face disasters without assistance.

Assume, "it is best for us to face disasters without assistance" is a good reason to allow evil.

If "it is best for us to face disasters without assistance" is a good reason to allow evil, then we should abolish modern medical care and fire departments.

But we should not abolish modern medical care and fire departments.

Therefore, "it is best for us to face disasters without assistance" is a not good reason to allow evil.