Because I'm that guy, I procrastinated on my apologetics homework by going to reddit and, well, doing apologetics. The question raised was, why not polytheism over Christianity? This was my response.
I always recommend books first: Reasonable Faith by William Lane Craig, or Miracles by C.S. Lewis.
To be honest, few rational thinkers believe those polytheistic religions offer any sort of cogent system. Note, I said polytheists- pantheists, such as Hindus, do have some apologists. Pantheism is a self-defeating proposition, but that's not what we're talking about here. Let's go back to polytheism. You'll have a hard time finding a core religious doctrine, let alone a philosophical or metaphysical (not the same as cosmological) component in those systems you mentioned. They lack any argumentative premise to even support or defend; they offer nothing but cool tales.
Unlike animism or polytheism, monotheism is a reasonable proposition. Let's begin, simply, with everything: the matter of existence. Our working concept here is that "everything that exists has a cause."
Let us suppose that you and I exist. (If that's a point someone would like to argue, they are free to argue it with themselves- I have no interest in debating a person who does not exist.) You and I have origins, a cause- we came from somewhere. For the sake of conversation, let's just assume we're merely evolved forms of electrified soup. That soup came from somewhere. The planet on which the soup simmers came from somewhere, as did our solar system, galaxy, and lo, even the universe.
Or did it? Did the universe have a cause, or is it, as Sagan says, all there is? It is either caused, i.e., dependent on another for existence, or uncaused, i.e., independent in its existence, not subordinate to anything. Evolutionists argue it is uncaused. Ignore them like they ignore physics. Science tells us there is a finite amount of energy in the universe and that it is constantly decreasing. "Heat death" is that glorious term for when the universe, our plane of existence, runs out of workable energy. So now we have a problem: were the universe uncaused, it wouldn't be finite. An uncaused existence isn't in danger of choking itself to death. The universe, too, is a finite reality dependent on a more powerful cause.
Further, if, the universe is uncaused and its existence is infinitely long, we run into the problem of infinite regress. So you and I exist. We had a beginning. The universe exists. It had a beginning. We call that the Big Bang. But maybe, just maybe, the universe's existence is an endless cycle of Big Bangs and Heat Deaths? That makes us ask where the energy comes from for the next Big Bang after Heat Death, but we'll ignore that in favor of a much more fun problem. An infinitely self-existing temporal reality is also infinitely long. There is an uncrossable infinity of time. Now, this is not the same as saying there are infinite subdivisions of time within a single hour, or infinite subdivisions of length in a mile. This is an actual infinity. Let's say you're in a library of infinite books. You trace every single novel with your finger, and just when you get to the end, there's another. And another. And another, ad infinitum. If it was your job to touch every novel before you went home, you never, ever, would go home. Actual time functions the same. Between today and the Big Bang, there would be infinite yesterdays. Infinite novels to be touched. Today would never arrive. Infinity cannot be overcome. You’d never come home.
So, it's a reasonable proposition to state the universe is neither uncaused nor an infinite existence. We move on to say, then, that it had a cause. There is a principle cause of the universe. I must stress here that everybody is prepared to admit an uncaused First Cause. Naturalists say the universe itself is the uncaused First Cause, that there is nothing above nature. But that's improbable, as we've shown. Supernaturalists say the universe is caused by a supremely powerful force external to the universe, which is more probable. Monotheists call this force, this entity, "God." What caused God? God is uncaused, the First Cause, just as the naturalists say the universe is. And that First Cause must be unified and supremely powerful; if it is subdivided into separate entities (which the Trinity is not; ask your local theologian) or if it is subordinate to another cause, then we’re merely pushing back the problem of fundamental existence. Somewhere, somehow, there is a supreme, unified First Cause.
So what in the flying-whoopity-whoop-whoop-doo does any of this have to do with tree gods and water nymphs? As we’ve seen, the universe is likely a dependent reality owing its existence to a single, supernatural (i.e., above nature) First Cause. If there were a god of the sea, a god of volcanos, and a god of spaghetti, etc etc, they would not be equal to, or a part of, the supreme First Cause. They would be subordinate, and therefore, not God. They’d be in a similar class as angels and demons; creatures of spirit, but not the Spirit himself. Or, perhaps, magicians: creatures of the material universe, but with a little more pizazz.
So why couldn’t there be hundreds of little demi-Gods running around the planet? Because there’s no real reason to believe that other than “it’d be so awesome.” What historical doctrine can you base that off of? None. I love reading those old mythology stories, but I can’t pretend that they’re in any way comparable to the logic of monotheistic religions. You assert that there’s little “real world evidence” to believe Christianity, which simply isn’t true on a dozen accounts. Propositionally, we’ve demonstrated that monotheism is more credible than polytheism, and that supernaturalism is more likely than mere naturalism. Christianity, too, has serious philosophical (and historical) legs.
On that point, we must believe that the supreme First Cause not only created the universe, but also interacts with it. We call those insertions “miracles.” But I’ve gone on way, way too long already. I insist that anyone curious about that proposition go read C.S. Lewis’ Miracles. It’s one of his toughest works, being purely philosophy. It’s also oddly prescient; I read Miracles right after Dawkins’ The God Delusion, and I found that Lewis anticipates Dawkins’ arguments by sixty years and deals with them handily.