It is a tenet of meta-ethical subjective relativism that ethical statements in general are true relative to some subjective entity or entities. In other words, ethical statements are statements not about the "objective" world (i.e. the world outside peoples minds) but about the minds of various entities. As such, seemingly contradictory ethical statements are simply statements about the properties of two different entities, and we are typically not philosophically distressed when different entities have different properties. We do not see a contradiction when we say that "Alice is tall" and "Bob is short." Similarly, the statements, "Killing Jews is good," and, "Killing Jews is bad," are not in contradiction, because they are statements about the different properties of different minds.
The subjectivist account really can't be understood as establishing a pattern of logical entailment. Subjectivism cannot attempt to establish the syllogism
Minor Premise: I dislike killing Jewsbecause of the rather obvious contradiction that different people really do have radically different likes and dislikes, which would entail that mutually contradictory statements would be accepted as true. The subjectivist position can't be that "Killing Jews is bad" follows from "I dislike killing Jews;" instead, the subjectivist position must be that the statement, "Killing Jews is bad" is the same statement as "I dislike killing Jews." A subjectivist theory is not a theory about how to find ethical statements objectively true or false, it is a theory of what moral statements mean.
Major Premise (enthymeme): What I dislike is bad
Conclusion: Killing Jews is bad
Now it is of course true that a lot of people really do intend an objective meaning by ethical statements. In contrast, when people say "Ice cream tastes good," they consciously and intentionally understand that they really mean "I like the taste of ice cream." In this case, the apparently objective syntax ascribing a property to ice cream itself serves only as a metaphorical idiom for the more literally accurate subjective language. But people typically don't have this idiomatic metaphor consciously in mind. Whey they say, "Killing Jews is bad," they really do mean that it is objectively true that killing Jews is bad, regardless of anyone's preferences; it is merely a happy accident (or the consequence of the objective truth) that they also dislike killing Jews. The subjectivist therefore sees the conscious meaning as a category error, an error that can be corrected only by applying idiomatic interpretation.
Whether subjectivism in general and this particular flavor of subjectivism is actually true at the meta-ethical level is a different argument. It might be true that "Killing Jews is bad" really is objectively true regardless of what anyone or everyone actually thinks. It might be true that "Killing Jews is bad" really does follow from "I dislike killing Jews." To date, however, I've been unimpressed by the arguments for either position. More importantly, I think subjectivism has a compelling positive case (which I've described in previous essays). Until someone comes up with a compelling epistemic theory that can give us any knowledge at all about the mind-independent truth of of ethical statements — a theory which, as far as I can tell, would be as revolutionary an epistemic innovation as was the scientific method — I have to go with the simpler theory that when we make ethical statements, regardless of category errors we might make in our interpretation, we cannot be talking sensibly about anything other than our own preferences.