The correct option is
A For
Option A: 'For' indicates purpose or reason. The given sentence states the reason behind why the professors disliked 'him': he was determined to think for himself and test the practical experiments based on the theories they taught him. They disliked him because he tested their teachings.
Hence 'for' adds a suitable meaning and option A is correct.
Option B: 'So' expresses result: he yelled at her, so she left.
Option C: 'But' expresses a contrast between two ideas.
Option D: 'And' means addition. It merely adds two words, phrases or clauses.
These words do not complete the sentence in meaning. Hence options B, C and D are incorrect.