Why Do Neutrinos and Anti-Neutrinos Oscillate Differently?

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They don't. The article was just wrong, and the reporter didn't know what he was talking about.
 
Why do neutrinos and anti-neutrinos oscillate differently?
Whether they do or not, and if they do, why, is a long-standing unresolved issue. The LSND neutrino oscillation experiment back in the 1990's seemed to see an excess oscillation from anti-muon neutrino to anti-electron neutrino. More than was expected, and difficult to explain. The MiniBoone experiment which ran from 2002 to 2005 looked at muon neutrino to electron neutrino, and to everyone's relief did not see an excess. But then they switched to using antineutrinos, and got a result confirming the one from LSND! This seemed to imply that neutrinos and antineutrinos behave differently.

See here and here for a summary.
 

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