The statements are self-explanatory.
First, yeah, my favorite episode of trek ever is The Cage. Period. End of discussion. it has my favorite characters and favorite story. I can't state it any more plainly. What, is it confusing because I'm not bowing at the altar of "City On The Edge Of Forever" or something? Sorry, I don't do that.
Second, look up the word "derivative." Everything in Trek's DNA, all the stuff that distinguishes trek from the other space franchises, the transporters, the warping, the "one ship, one crew," the "guy with the ears," - the source for all of it is The Cage, which makes The Cage the original work and everything else derivative of that original work.
Of course, The Cage is derivative of Forbiidden Planet, which in turn is just the sci-fi version of The Tempest, but its place in the Lineage of Trek is always "First," and I'm down with that.
It just surprised me because I certainly think there are other episodes that are better than the Cage, and if you polled the fanbase on what everyone's favorite episode was, I bet The Cage wouldn't win. You, of course, are allowed to have any episode as your favorite. It's an unusual choice. I think I'm allowed to be surprised by an unusual choice. For the record, COTEOF isn't my favorite either.
In my mind, The Cage, along with every other episode of TOS is all part of the same unit. It's all the same series, so it seems odd to me to say some episodes of a series are "derivative" of another episode in the same series. So are all the episodes of a series "derivative" of their pilot? Is the pilot of any series your favorite because it was The First?
It's like you're saying The Cage is its own separate entity separate from the series. Doesn't make sense to me.