Isn't the only reason the Supreme Court would not sustain a law is because it is unconstitutional? And otherwise their only role is to interpret laws? At least that's the way it is supposed to be AFAIK.
No, the court can also say that two laws are inconsistent. In this case, there is a judicial ruling (Chevron) that has stood for a while, that they are saying is inconsistent with a law (the APA). The constitution is not in this ruling at all. Generally, laws override judicial rulings unless the constitution is in question.
Can the Supreme Court ever declare two Constitutional clauses to be inconsistent?
I doubt it, but I'm sure they can "interpret" them to consistency.
But that’s not really how it works, is it? The court is more interested in pushing an agenda than playing its role in balancing the other branches of government. It’s obvious in the way they defer to precedent when it suits them and throw it aside when it does not.
Nevertheless, the constitution does forbid this, and the decision is correct.
Where exactly does the constitution forbid “this”?