No, but you made an absolute statement. I refuted it. Easily too.
Be careful with "all", "must", "have to be".
I did state that they generally are lawyers, but it's not a requirement, even at the Supreme Court.
IMHO, it ought to be a disqualification above the level of trial judge. Let them have lawyer advisers. Lawyers are trained to manipulate the laws to their advantage, or that of their clients, rather than to enforce them, which is the job of judges and justices.
I provided the definitions of lawyer and judge in the statement that I made. One has to be trained in the law in order to be a judge.