1: a majority (5 out of 9) of the judges on the court were appointed by presidents that weren’t duly elected: one was appointed by an earlier SCOTUS stopping legal ballots from being counted and the other was proven to engage in a vast election fraud conspiracy with foreign adversaries. Even after all that cheating, neither won a majority or even a plurality of votes.

2: One of those 5 and one of the remaining 4 were appointed in spite of credible accusations of serious crimes. In neither case, those accusations were seriously, thoroughly and independently investigated. In one of those cases, the reaction revealed a thin-skinned, hot-tempered and vindictive demeanor unfitting of the most local judge, let alone one of the highest court.

3: One of the above likely sexual offenders is a wholly owned subsidiary of Billionaires’ Every Whim LLC and the rest agree with the servant of nazi memorabilia collector Harlan Crow that no real consequences for or even reporting of ethics violations by themselves would be appropriate.

4: Another of the 5 appointed by illegitimate presidents belongs to a theocratic cult that considers religious law to supercede the secular law the courts are tasked with interpreting and shaping, making her by definition biased in favor of theocracy and against the establishment clause of the first amendment.

5: Almost all of them have neglected to recuse themselves from at least one case where they had a conflict of interest, some of them dozens if not hundreds of times

There’s probably more reasons, but those are the most obvious and indisputable ones, each of which is in itself sufficient to at the very least cast doubt on the legitimacy of the court.