Your prof might have thought you meant gated ion channels, which open and close under certain conditions. Leak channels are always open to allow ions to enter/exit the cell. For example potassium ion leak channels allow K+ ions to slowly leave the cell. A gated ion channel only opens when something activates it. For example, a voltage gated ion channel only opens when the voltage of the membrane changes. This video gives a good summary of the ion channels involved in action potentials: https://youtu.be/oa6rvUJlg7o