Is worship of Shiva equivalent to worshiping death, destruction, and catastrophe?
Shiva is the deity associated with the guru and soul-liberation. Shiva represents death of the ego, the small self. Death of pettiness, death of attachment to material desires. The yogi sees Shiva as representing the expansive quality of release from all limitations in order to fully embrace God-realization.
The guru is the one who frees the soul from material bondage of every sort, and so Shiva is associated with the guru.