The word arrogant means 'a sense that one is more important or able than one actually is'. For example, 'The boy is quite arrogant.'
Option A: 'Humble' is the opposite of arrogant. It means 'having modest or low estimate of one's importance. Hence A is the correct option.
Option B: 'Cowardly' means 'lacking courage'.
Option C: 'Egoistic' is a person who is self-centered and is always preoccupied with oneself.
Option D: 'Gentlemanly' is a person who is chivalrous and is honourable in his manners.
These options are not related to the word 'arrogant'. Hence options B, C and D are incorrect.