Answer
Animals need faster signals because, with their muscles and skeletons, they react much more quickly than plants generally do. Plants much more commonly respond by growth which is vastly slower than the muscular movements of animals.
Work Step by Step
Imagine: You turn a plant on its side, and it takes some days for the stem to bend, by growth, back towards upright. You put a cat on its side, and it is upright again in less than a second. There is the difference between plants and animals which drives the difference needed in signaling speed.
