How does the Big Bang Theory make sense?

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Okay, so I recently took a Geology class that had an emphasis in the Big Bang Theory. I've also taken Chemistry, Biology, and other science classes that have all had an emphasis in the Big Bang Theory. Through all of these classes, I have wanted to know one simple thing: how does this theory even make sense? So, let's go over some of the Big Bang Theory proof that scientists have. First, let's start with Carbon Dating. Now, I'm not saying I'm an expert in Carbon Dating or anything, but here's what my teachers have told me. Basically, a scientist can date an object on the half-life of Carbon. They figure this out by figuring out how much of the parent product is left compared to the other product with some other mathematical stuff I never really paid attention to. The half-life of Carbon is roughly 6,000 years. I can't remember the exact number, but the point is that it was far higher than any human lifespan. Who was around to tell us that these Carbon molecules deteriorated this way? So many other factors could have come into play to make these molecules deteriorate faster or slower. Scientists assume with Caron Dating that the molecules simply deteriorated at an average rate. Nothing deteriorates at the average rate. Secondly, we have the fact that the universe is expanding. They can prove this by the red shifts in things, which I could see as a possibility. I'd have to look more into red shifts and everything to really see if the universe is expanding, but whether it is or not is the point. The point is that the scientists state the age of the universe by taking the AVERAGE RATE of expansion and counting backwards. Once again, we have this problem with the average rate. Their idea is that the universe began as a ball of matter that exploded. Things that explode usually tend to move faster then start to slow down. The average rate that our universe is moving at now is probably much, much slower than it was when it first blew up. If you even believe the universe exploded to make everything, that is. Scientists came up with a billions-of-years age for the universe. Who was alive in this time to prove our universe is that old? All in all, my personal belief is that this theory is completely based on other theories that seem to rely on the basis of the Big Bang Theory. Does anyone else see the circular logic? A theory whose proof is other theories that rely on this theory to be true in order to be true themselves... Hmm. It's definitely something to think about as scientists learn more and begin to realize that the Big Bang Theory is slowly but steadily becoming less of a possibility.