why is it not accepting 'He did not believe him at first' ?
le can mean him, right?
I think "wouldn't believe" is the conditional tense which is conjugated thus: "Il ne croirait pas ..." However, sometimes 'would' does translate into the imperfect tense in the sense of "I used to = I would." So if you said "Je allais au restaurant = I used to go to the restaurant" it can also be translated as "I would go to the restaurant" but in this case has the meaning of 'used to' rather than the conditional 'would'. (i.e., I would go if I had enough money) Sorry to flog the point so much but it's a nice subtlety to think about.
"Would" is not just a conditional term. It is also used in English to reflect the French Imperfect tense when it refers to a habitual action in the past. E.g., Nous allions à la plage tous les jours = We would go to the beach every day. So in this sense, "He would not believe it at first" should be fine. Perhaps Duo choked on the contraction "wouldn't".
"He was not believing him at first" should be accepted too and with more credentials than the "correct" answer.