That cup of water represents a person's normal mentality. And the mud represents the demonic bloodline of the Tohno family. Now if mud had happened to fall into that cup, then it would completely change the structure of the water. That would make it undrinkable.

... What I'm trying to say is that the other Tohno Shiki that day went insane. His demonic blood awakened by random chance and he tried to attack Akiha. But I ended up protecting her which is why I have that scar.