Subjectivism in Ethics
The basic idea of ethical subjectivism is that moral judgments are fundamentally subjective, i.e. based on feelings. This says nothing about what is right or wrong. So subjectivism does not allow (or forbid) anything, and it is nonsense to talk about how things would be if subjectivism were our guide or were put into practice. So you cannot criticize subjectivism by talking about the bad effects it would have. It is (meant to be) merely a description of the meaning of words such as 'right' and 'wrong'. It either gets the meaning right or it doesn't. So it is true or false, not good or evil.
Simple Subjectivism: What does it mean to say that ethics is subjective? The simplest version of the theory says that if you say "x is wrong" then what you mean is "I disapprove of x." In other words, you are reporting on your own attitude. It is hard to imagine anyone being mistaken about their own attitude (e.g. thinking they are pro-life but really being pro-choice), so if simple subjectivism is true then nobody who says "x is wrong" is likely to be wrong. This sounds strange. If someone says "Courage is bad" aren't they wrong? Well, it depends what you mean by 'wrong'. If you mean morally wrong then subjectivism does not say. Remember that it is not a theory about what is right and what is wrong. According to simple subjectivism people are only infallible in their moral judgments in the sense that people cannot be mistaken about what they feel is right or wrong. Strange as it might sound, this could well be right. After all, a mistake is a kind of accident, and people's beliefs about ethics might be misguided but they are surely never accidents. So perhaps we really cannot be mistaken in our moral judgments.
Another curious feature of simple subjectivism is the idea that what seem to be moral disagreements, according to this theory, really are not disagreements at all. Why? Because if one person screams "Allowing abortion is wrong!" and another screams "Allowing abortion is right!" then, according to simple subjectivism, what they mean is "I'm against allowing abortion!" (which is true) and "I'm for allowing abortion!" (which is also true). Either one might be morally wrong or in error, but neither is incorrect or making a mistake (as long as they scream sincerely).
So simple subjectivism can be defended up to a point. However, it does sound wrong (i.e. mistaken) to say that what are generally called moral disagreements are not really disagreements at all. And what if someone says something like "Bullying is cowardly"? That does not just mean "I'm against bullying." It means that bullying shows or involves a deplorable lack of courage, an unwillingness to overcome fear (by, say, picking on someone one's own size). The 'deplorable' part might be subjective, but the rest of this judgment does not seem to be. So simple subjectivism does not seem right when we move away from very abstract and general terms like 'right' and 'wrong' (which Bernard Williams has called "thin" concepts) to focus instead on richer, more specific ("thick") concepts such as courage, honesty, cruelty, etc.
Emotivism: An alternative form of subjectivism that avoids some of these problems is emotivism. According to this theory "x is wrong" is not a report on the speaker's feelings, so it is not infallibly correct. It cannot be correct or incorrect, because it is not a statement of fact but an expression of emotion, like smiling or crying, which are not correct or incorrect either. If one person says "capital punishment is wrong" and another says "capital punishment is right" they are not disagreeing about a fact, because, according to emotivism, they are not trying to state facts at all. They are emoting. But there is a kind of disagreement here all the same. It is disagreement in attitude (i.e the two people have different attitudes towards capital punishment). This part of emotivism sounds like an improvement on simple subjectivism.
However emotivism still has its problems. It sounds perverse to deny that "The Soviet Union under Stalin was a repressive regime" is a statement of some kind. It might be said with emotion, but it is not just an expression of emotion. True, 'repression' is an evaluative concept, but it is not merely evaluative. Empirical evidence could be cited to back up the claim. Again, if we reject thin ethical concepts in favor of thick ones the theory comes to seem much less plausible.
Conclusion: It does not follow that subjectivism itself is wrong. It is very hard to imagine ethics without emotion. We might be able to prove purely objectively that a certain act was unjust (e.g. we could prove that the convicted man was innocent) or brave (there really was a present danger, she knew about it, but she pulled the archbishop out of the burning building anyway). But can we prove that it is good to care about justice or bravery at all? We might be able to prove that it is useful to have these values, but is it right to reduce ethics to the art (or science) of what is useful? Besides, the very idea of usefulness implies some end to which the useful thing is a means. But what ends (i.e. goals) should we have? Can that question be answered without any reference to human feelings? And, can we even understand the idea of, say, courage, without coming to feel that it is a good thing? Doesn't knowing what to call 'brave' or 'repressive' or 'indecent' etc. involve having a certain subjective reaction to acts of the appropriate kind?
You might think so, or you might not. If not you might want to embrace objectivism. For the problems that theory faces see Relativism, Objectivism and Subjectivism.