Multi-Agent Debate (MAD) has emerged as a promising inference scaling method for Large Language Model (LLM) reasoning. However, it frequently suffers from belief entrenchment, where agents reinforce shared errors rather than correcting them. Going beyond merely identifying this failure, we decompose it into two distinct root causes: (1) the model's biased $\textit{static initial belief}$ and (2) $\textit{homogenized debate dynamics}$ that amplify the majority view regardless of correctness. To address these sequentially, we propose $\textbf{DReaMAD}$ $($$\textbf{D}$iverse $\textbf{Rea}$soning via $\textbf{M}$ulti-$\textbf{A}$gent $\textbf{D}$ebate with Refined Prompt$)$. Our framework first rectifies the static belief via strategic prior knowledge elicitation, then reshapes the debate dynamics by enforcing perspective diversity. Validated on our new $\textit{MetaNIM Arena}$ benchmark, $\textbf{DReaMAD}$ significantly mitigates entrenchment, achieving a +9.5\% accuracy gain over ReAct prompting and a +19.0\% higher win rate than standard MAD.