Why are most galaxies/solar systems 'flat'?

Why are most galaxies and solar systems 'flat'? If there is a cloud of
dust/gas that starts to coalesce around a localized density in the middle of
the dust/gas, it seems it would attract from all 3 dimensions equally. But
galaxies and solar systems attract primarily in a single plane. What
happened to all the debris above/below the plane?

I understand there will probably be an unequal distribution of matter
surrounding the central object and there will consequently be a resultant
angular momentum after a while. But that doesn't seem to explain why there
still isn't debris spiraling in from above/below the primary plane.