Taking off from the moon to go to mars would take less fuel but ignores the fact that we have to take off from earth first. You either take off from earth and go to mars, or you take off from earth go to the moon and then mars. To skip taking off on earth requires us to build out mining, manufacturing, and ship launching stations on the moon. All monumentally more difficult than just fueling up in earth orbit.

The trip to mars is not safer or easier by building out manufacturing and mining on the moon and then doing cryogenic transfer in deep space. Much safer to use earth resources and cryo transfer in earth orbit where if something goes wrong it can more easily be rectified.

There's a few ways to skin a cat but that doesnt mean they're all equal for the current tech level.