Why did Sai believe that feeding a black dog would help Balasaheb Deo read the Dnyaneshwari?

Your question is based on a premise that is not supported by the provided information from Chapter 41. The text makes no mention of Sai suggesting that feeding a black dog would help Balasaheb Deo. The source material explains that Deo's difficulty with reading the Dnyaneshwari was a long-standing issue, where obstacles would always arise and doubts would make his reading superficial. His solution, as described in Chapter 41, was to make a firm resolve to only resume reading the Dnyaneshwari after receiving a direct order from Sai Baba Himself, placing his faith entirely at Sai’s feet.