It's not just the center of gravity. I think people really underestimate how hard landing on the Moon is, because counter-intuitively, the lack of an atmosphere makes things harder, not easier. Landing on Mars (or even Venus (!!) - which is the first other planet we ever landed on) is easy mode by comparison.

With the lack of atmosphere is that there is no 'natural' attitude/orientation correction. If you're tilted 5 degrees then you'll stay that way. With an atmosphere drag and aerodynamic forces can be used to ensure a proper orientation.

'Just make sure you come down straight' isn't so easy because when you enter the Moon's 'orbit' (not necessary, speaking colloquially) you're traveling extremely fast. And so to land you need to zero out your horizontal and vertical velocities. You do this by literally turning around the opposite direction and thrusting. And then you need to simultaneously also ensure your vertical velocity stays near zero as you approach the surface.

And then finally you need to come down with your vertical velocity at near zero, your horizontal velocity at zero, and perfectly orientated. This is really friggin hard. If you have even a hair of velocity you're going to bounce, skid, and otherwise do nasty things - which is why so many landers end up on their side, if not upside down. And then there's the Moon's surface itself. Come in on an even slightly unlevel terrain and again you're in for a wild ride.