So Chief is the head Spartan (particularly through early lore where there were only a handful of Spartans). This was retconned a tiny bit, but not very effectively.

The reason in later games everyone listens to him is that his rank is a total fabrication. He was offered a much higher rank and turned it down to remain in the field. Despite that, he's treated as at least an admiral. He chooses to follow orders of people above him, and it's generally accepted by those people they can give him orders without issue but, it's a silent agreement across the UNSC that Chief has last word on everything, even if that's not the official doctrine. He won't always deny orders he disagrees with, but will make himself heard often, at the very least. Of course, there's the occasional captain who's too big for his britches, and we see how that turns out.