Give a specific case where calling a polynomial time function n times gives an exponential time algorithm
A concrete example is repeated squaring. Squaring an integer of length $n$ takes time $O(n^2)$ (using the naive algorithm; you can do much better with more complicated algorithms). If you square an $n$-bit integer $i$ times in a row, its length becomes $2^i n$. So if you square it $n$ times in a row, the complexity is $O(4^n n^2)$, which is exponential.

The source for confusion is the input length. If the polynomial time function increases the length, then the behavior can be exponential. If it doesn't, the behavior stays polynomial.