In a sentence or two: why does a larger sample make a sample percentage less variable?
Write a little first — committing to an answer before you look is what makes this useful.
One way to say it:
Each individual observation is random, but in a large sample the random highs and lows mostly cancel each other out. For the overall percentage to land far from the truth, many independent observations would all have to lean the same way at once — and that gets less and less likely as the sample grows. (Formally: the standard error of a proportion shrinks in proportion to 1/√n.)