One, that isn't even a fact. A few of the early Justices were confirmed before formal legal education existed in this country. They practiced law but were self taught or learned through apprenticeship. It's only technically wrong but still facts are facts.
Two, objective facts are proven, not strongly indicated which itself is subjective. The fact that all Justices have been attorneys indicates to me, that the Senate has largely believed, subjectively, that experience with the law is important for Justice to have.
If we want to know objectively what criteria one needs to be a Justice we need only to look at the requirements laid down by the Constitution for it sets the legal requirements and objectively, it makes no requirement of formal legal education. If you believe otherwise, prove it.
No I don't. The Constitution has given you your answer.
There are objective criteria. You have to be nominated by the President and confirmed by the Senate.
Race and sex are irrelevant criteria according to law but law is implemented by people, in this case the President and the Senate. If those two bodies believe subjectively, that diversity on the court matters then race and sex become objectively important to achieving that goal.
What you seem to be failing to understand is that context matters. Something can be both subjective and objective depending on the context. For instance my love of oxtail is subjective but objectively I do love it. Make sense? Probably not. But it amusing watching you try and try and try....