"Plants don't die from cancer" for the same reason "plants don't scream": These are human created concepts that are rooted in humanocentric mental models and plants fail to conform to our conceptual framework. It's much the way sexism, racism etc work.

Reality: Plants give off a pulse when attacked. Human ears don't "hear" it, so we don't count it as "screaming." They also communicate chemically with nearby plants when they get infested with hostile insects. You could say they put out the word and nearby plants of the same species act to protect themselves.