Due to the fact that Greg wrecked his family's station wagon during a road trip last summer, he has not beeb and probably never would be allowed to drive his father's car
A.has not been and probably never would be allowed to drive.
B.has not been allowed to drive and probably never will be allowed to drive.
C.has not and probably never would be allowed to drive.
D.has not and probably will never be allowed to drive.
E.has not and probably never will be allowed to drive.

I am not able to understand what concent is tested here. Please explain why are other answer choices wrong

This is a tense and parallelism issue.

He has not been allowed to drive since the accident, and he probably never will be allowed to drive from this point forward.
The key is that "to drive" has to go with both parts, which rules out C, D, and E -- they're all missing "been" in the first part.
We also don't want to say "would be allowed" since we're talking about future here, rather than a conditional time -- he will not be allowed to drive from this point into the future.

This leaves us with B, which seems redundant at first reading, but is the only one grammatically correct.

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