I'm a high school student and acknowledge that my understanding of this concept may not be as in-depth as that of more experienced physicists, and I welcome any corrections or additional insights on this topic.
When two opposite mechanical waves interfere destructively, it means that the crest of one wave overlaps with the trough of the other wave. In this case, the amplitudes of the waves add up to zero at the point of superposition, which means that the displacement of particles from their equilibrium position is zero. When the particles have zero displacement, they have zero velocity and hence zero kinetic energy. Therefore, at the point of superposition, the particles have zero energy and zero intensity.
It is true that as the waves move apart, the particles will gain kinetic energy and the intensity will increase. However, at the point of superposition, where the waves are cancelling each other out, the particles have zero kinetic energy and zero intensity. This is because the energy associated with the wave has been transferred to another region of space, where the waves interfere constructively, and the particles there have a higher energy and intensity.