> Why is this bad?
That is an excellent question. Part of it comes down to the fundamentals of ethics. If I believe, for instance, that the bedrock of ethics is "do whatever is best for me" and I happen to be one of the rich folks, then this may not seem so bad. If I take as one of my basic ethical principles "From each according to his ability, to each according to his needs." then a high Gini index is patently unfair.
If the answer depends on what basic principles of ethics you accept then in a certain mathematical sense there is nothing to say here. Once a proposition has been proven to be true or false depending on what axioms you use, there is no sense in proving things anymore, we can just argue about which axioms we like best, or perhaps just stop discussing it. Philosophers have spent (literally) centuries arguing over what fundamental principles to base ethics on, and nothing has been permanently settled.
But I will make this observation. Human beings seem to have a basic, built-in sense of "fairness". Researchers have conducted experiments where two participants are given something (like cash) and one picks how much to take, then the other decides whether both get their amounts or get nothing. Many (perhaps most) participants will split it 50-50. More interestingly, if the first player splits it 95-5, the second player will usually get indignant and decide that both will walk away with nothing. Most humans would rather give up a free $5 in order to prevent someone else from getting "more than their share".
Now, I can't say whether you are one of the people who would act that way -- as mentioned before, different people have different takes on the fundamentals of ethics and I don't know what moves you. But this example may help you to understand why many people have a visceral distaste for high Gini indexes.