The court system is better suited to protect the induvial instead of elected branches of government. The court runs on laws and constitutional rights, judges make their decisions based off of these things. While on the other hand, elected branches from congress to the mayor of NYC act somewhat like a popularity contest. Whatever side supports them more with reach and funds is the side that gets their concerns addressed first with elected officials. An example of this would be the recent NYC mayoral election. Andrew Cuomo was a mayoral candidate that was funded by a super PAC that he would ultimately get in office to cater to. Judges don’t cater to people in cases for the money.
I would say the Supreme Court is anti-democratic in structure, but not necessarily anti-democratic in purpose. It is anti-democratic in the sense that it is intentionally shielded from direct elections, yet that shield is meant to protect democratic principles like equal rights, fair trials, and constitutional limits on government power. In other words, the Court is designed to stand against majority rule when majority rule threatens constitutional freedom.