Actually, race, social status, sex, etc., are all factors. Which is why there is jury selection isn't just random and is determined in part by the defense. However, speaking personally, I don't want a jury of my peers. The prosecution's job is to convince the jury the evidence says one thing. The defense is there to say it means something else (or, at the very least, that there is a sufficient amount of doubt concerning what the evidence says). They can do this by trotting out paid experts who will say whatever they are paid to say (not necessarily because they are lying, but perhaps because they are specialists in some field where there is not a great deal of agreement in the area about which they are testifying), they can use rhetoric, they can use charm, and all other kinds of evidence which rely on fallacious reasoning or are otherwise without logical soundness.
And the jury, without any training, without any knowledge of the law other than the little bit they are informed of by the judge and are (mis)informed of by the prosecution and/or defense, is supposed to use the fact that they are my peers, rather than, for example, a group of people who are (like judges) part of the legal system, paid by the government (perhaps elected) to learn the legal system and to be "jurors". The idea behind "jury of peers" (whatever it was, and as I've no interest in evaluating those who argue that it was not intended to be fair but to legitimize, or justify, a particular system without actually doing so) is rather fundamentally flawed. Or, at the very least, it has created a legal system in the US in which the prosecution and defense "win" by putting on a better show. My "peers" are not qualified (because I am not qualified) to understand the nuances of legal proceedings, laws, and the system itself such that for a given trial in a particular district, they (or I) would be able to tell when one side was putting on a better show, but that this was all it was.