Why does a cumulative frequency graph never go down?

Because of the word "cumulative". What that means is that the height of the graph for any value (X=x) is the number (or proportion) of observations that were less than or equal to the value x.

Now consider the cumulative value of the graph for a value of X which is bigger than x. All the previous observations were ≤ x and so they will be ≤ the newer, larger value. So the height of the cumulative graph cannot decrease. It may increase if there are any observations whose value was between x and the new value.