A clash between mind and emotions is a clash between two assessments, one of which is conscious, the other might not be. It is not invariably the case that the conscious assessment is superior to the subconscious one; that needs to be checked out. The point is not that we follow the voice of emotion or feeling blindly, it means only that we don't dismiss our feelings and emotions so quickly; we try to understand what they may be telling us; we don't simply repress, rather we try to resolve the conflict between reason and feeling. We strive for harmony, for integration. We don't simply slash away the pieces of ourselves that don't fit our notion of the good or the right or the rational.
The solution for people who seem over preoccupied with feelings is not the renunciation of feelings but rather greater respect for reason, thinking, and the intellect. What is needed is not a renunciation of emotion but a better balance between emotion and thinking. Thinking needs to be added to the situation, emotion does not need to be subtracted from the situation.