The detection of mental health problems from social media and the interpretation of these results have been extensively explored. Research has shown that incorporating clinical symptom information into a model enhances domain expertise, improving its detection and interpretation performance. While large language models (LLMs) are shown to be effective for generating explanatory rationales in mental health detection, their substantially big parameter size and high computational cost limit their practicality. Reasoning distillation transfers this ability to smaller language models (SLMs), but inconsistencies in the relevance and domain alignment of LLM-generated rationales pose a challenge. This paper investigates how rationale quality impacts SLM performance in mental health detection and explanation generation. We hypothesize that ensuring high-quality and domain-relevant rationales enhances the distillation. To this end, we propose a framework that selects rationales based on their alignment with expert clinical reasoning. Experiments show that our quality-focused approach significantly enhances SLM performance in both mental disorder detection and rationale generation. This work highlights the importance of rationale quality and offers an insightful framework for knowledge transfer in mental health applications.