Eugene definitely has his plusses, since he craftily used a dead woman’s iPod in an attempt to cause a walker distraction, which would have worked if it wasn’t for that meddling Dwight and his talking dog.
It’s his biological imperative to survive, after all.
In any case, Eugene has been given ample chances to show his allegiance to Rick’s crew, and all he’s done is get offended and get pissy about what he thinks doing the right thing is, which usually results in him defending his selfishness.