The correct option is B even though he has had a rough childhood
An adverb clause is a group of words containing a subject and a verb, and it functions as an adverb, by modifying an adjective, verb or an adverb. Adverb clauses generally begin with a subordinate conjunction (since, because, while, etc.).
Option B is correct because it is an adverb clause of concession or contrast, 'even though' is a conjunction that refers to the contrasting ideas: 'well-mannered and polite' and 'rough childhood'.
Option A is incorrect because it is an adverb clause of reason whereas the required clause must be of contrast.
Option C is incorrect because it is a coordinate/independent clause whereas an adverb clause is subordinate/dependent.
Option D is incorrect because the answer lies in B.