The word 'never' expresses a habit, in the negative. Hence, the correct verb must express the relevant tense.
The simple present tense expresses a habit or custom, so the required verb must be of that tense.
Option A: 'Drink' is a simple present verb. It indicates that the subject does not drink coffee. Hence option A is correct.
Option B: 'Am drinking' is in the present continuous. It expresses an action that is happening at the moment. It does not express a daily habit.
Option C: 'From a cup of' does not state any action. As a result, the sentence is left incomplete, because there isn't any verb.
Option D: 'Drinking' is a present participle. Participles are verb forms; in order to express any tense, they require helping verbs (have, is, am), without which they cannot state any action. This word isn't suitable for the given sentence.
Hence options B, C, D are incorrect.