Contrite means to be regret one's action. Obdurate means to refuse to change one's views. The 2 words are antonyms.

Let us evaluate the options.

Option A:
Grievous means to do something bad and severe. 
Lamentable is a term used to denote that the action is bad or deplorable. 

The 2 words are synonymous. 

Option C:
Sophisticated is a term used to describe a high degree of development. 
Cultured and sophisticated cannot be termed antonyms. 

Option D:
Assenting means to give the nod. Favourable and assenting cannot be termed opposite in meaning. 

Option B:
Aphoristic is a term used to describe that the claim is a general truth or widely accepted.
Esoteric is a term used to denote something that is understood by a limited set of people.

The 2 terms are opposite in meaning and hence, option B is the right answer.