Correct me if im wrong - Cyclebutane is puckered because all the carbons are SP3 so they want to be 109.5 bond angles but can't be because its arranged in a square, which we know has 90 degree angles on every side. Oxetane is virtually flat because the oxygen has two lone pairs rather than hydrogens so it can flex a bit more to flatten out the ring. And actually the electron groups can push the bond angle to be smaller like they do in H2O which has an actual bond angle of 104.5.
Edit: it would be easier to understand if you made the molecules with a model kit
Edit 2: im wrong.