In my opinion, both sentences are absolutely fine. The first one is perhaps more 'sophisticated/advanced' English as it contains a nice linking word 'although,' as well as 'fond of,' which is a great alternative to 'like.' However, that does not mean that sentence B is not acceptable. We could improve sentence B by saying 'He was the strictest teacher in the school, but was still liked by everyone.'

Sentence B is fine. It has the same meaning as sentence A and it's OK grammatically. If anything, sentence B sounds more natural than A. You should not have had this marked as incorrect.

I believe the problem might lie in the use of the conjuctions. Was there anything else in the question? About the conjunctions... "Though" is a subordinating conjunction and "but" is a coordinating conjunction. Even though both sentences are gramatically perfect, there is a slight difference in meaning. When a clause follows subordinating conjunctions, it becomes a subordinate clause, which needs a main clause to make a complete sentence. This means that "Though he was the strictest teacher in the school", by itself, does not make much sense. Coordinating conjunctions connect items which are the same grammatical type, e.g. words, phrases, clauses, and this means that, by themselves, they have complete comprehensible meaning! I hope I have been useful to you!