Why fast neutrons for breeder reactor but slow neutrons for regular light water reactor? Water is used as a moderator to slow down neutrons in a light water nuclear reactor.  By slowing down the neutrons they have more of a window to strike fission ready nuclei thus promoting the self perpetuating chain reaction when more neutrons are released from the fissions and slowed neutrons.
All fine and good so far.  I got it.  Now, what I don't get is why fast neutrons are needed for the breeder nuclear  reactor.

According to my research, the main reason breeder reactors have not met expectations is the problems encountered with the liquid sodium cooling system. Why liquid sodium instead of water?  Because water is a moderator that slows neutrons, while liquid sodium does not slow down neutrons.
Why do we need fast neutrons to breed Pu 239 from U 238.  Wouldn't the same slow neutrons used in fission chain reactions also increase the probability of the neutron encountering and hitting the U238 nucleus? 
 A: I'll take a shot at this. Head over to the National Nuclear Data Center  hosted at Brookhaven National Laboratory. Go to the Evaluated Nuclear (reaction) Data File section (ENDF) where you can get cross section for various neutron reactions. 
Below I have put in a screenshot of the result of plotting 4 different reactions. 
The first, topmost, black line is the total cross section for neutrons interacting with $^{238}$U. 
The second, green line is the elastic scattering cross section, that is $^{238}$U(n,n)$^{238}$U - the neutron goes in and bounces off. 
The grey line is the cross section for neutron-induced fission - the neutron goes in and parts come flying apart. This of course does nothing to get to $^{239}$U and the path to $^{239}$Pu.
Finally, the (mostly) lowest red line is the cross section for absorption of the neutron (and release of a gamma), i.e. $^{238}$U(n,g)$^{239}$U. This is what you want in a breeder reactor.
One can readily see that below 1MeV, neutrons are (far) more likely to fission the $^{238}$U nucleus then make $^{239}$U. So, moderated neutrons are of no use at all for breeding Pu.

