why is U-238 more stable than U-235?

Answer 1

It is due to Proton and Neutron pairings.

U-235 has an odd neutron which makes the material fissile (i.e. it can undergo nuclear fission and it's nucleus can be split.)

U-238 has no odd neutron, so it is more stable, and IS NOT fissile i.e. it cannot undergo nuclear fission.

U-238 must be enriched if it is to be used as a nuclear fuel.

Answer 2

The answer to this question is more complex than simply saying that the extra neutrons stabilize the nucleus of U238. It has to do with the specific quantum states occupied by the various nucleons in each case and which quantum states are available, and the energy differences between the two. In U235 there exist available quantum states which differ from those occupied quantum states by only a very small amount of energy, and hence there is a higher probability that a nucleon may randomly find itself with the needed available energy and thus be ejected from the nucleus. This is even more probable if there is a low-energy neutron thrown into the mix (that's how chain reactions are started).