Emotional sensitivity is an important part of meditation practice. Sensitivity here doesn't mean fragility - it's a capacity for a much more present, subtle and detailed awareness of your emotional life. This actually leads to resilience, as we can understand our emotional dynamics better, and not be so taken by surprise by tidal waves of emotion that we didn't see coming.
Practicing in ways that include our emotional lives helps to ensure that we're not spiritually bypassing - attempting to reach some detached transcendent state in which our troublesome emotions are not present.
Instead, we can include everything - body, emotions, mind - in our process of deepening into a greater sense of presence, space and harmony.
Emotions