Opposing waves do not annihilate because their energy just shifts form.

Evidence

Figure 2.8b illustrates an interesting case where two waves of the same form but opposite polarity pass each other in opposite directions. It may first appear illogical that the waves do not cancel each other totally. Remember, however, that the energy of the waves cannot disappear; it is just in kinetic form in the middle situation and reappears as potential energy after passing. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 181

Categorization

• CANDY: A clean intuitive clarification of why two opposite waves passing don’t cancel out — a good way to explain wave energy conservation.
• XREF: connects to: Einstein proved light is simultaneously particles and waves, reconciling opposites. — Yanis Varoufakis, Technofeudalism: What Killed Capitalism, 56