Thanks for the interesting question! Here's my answer.

It's true: the Apollo spacecraft did not fly in a straight line. One way to see this is that the Moon is a moving target. So, when it was leaving the Earth, if Apollo aimed straight for the current position of the Moon, by the time it got to those coordinates, the Moon would be far away. After all, it took about three days to fly there, and the Moon orbits the Earth so quickly that it does a complete loop every 27 days. So if someone tells me that Apollo is traveling "on course," I would need to ask them if that means "towards the current position of the Moon" or "towards the projected position of the Moon in about three days."

There's a second part to this explanation, though. It turns out that Apollo was not traveling directly "on course" according to either definition! This is because the safest way to enter the Moon's orbit starts with "catching up" to the Moon and flying alongside it.

Let's look at the images in this analysis of Apollo's flight path.

From the first five images you can see that the entire path follows a smooth curve designed to safely enter the Moon's orbit. Since the Apollo is so small compared to the Moon, it needs to take special care to work with the gravity of the Moon to avoid getting thrown out of orbit or smashing into the surface. What is that special care? By the time the Apollo reaches orbit, it is already moving in the same direction as the Moon and it is offset slightly to stay in orbit.