Logistic Regression Cost Function Intuition start around 3:24

That sounds correct, but the point is that is just the first step. Then the question is, “ok, if that is your goal, then what is a function that can express that”. How does the log loss function help with that? Prof Ng goes on to explain that in the lecture.

Here’s a thread that shows the graph of the log function between 0 and 1 and discusses this a bit more.