Have you ever had someone slam a door in your face? It’s perhaps the clearest possible way of saying ‘I don’t want you here’. A door slammed shut means that you are not welcome here. An open door on the other hand is a sign of welcome: enter in here, and you’ll be made to feel at home.
When Jesus described himself as gate, he didn’t mean a locked gate with a ‘No Entry’ sign across it, He was talking about an open gate, a gate that allows all to enter and find a place to call home.