Natural Selection is common sense.
When there are too many organisms in an environment, will all of them survive? No. Who will survive? The "fittest". If a cheetah is really fast, how is it going to be eaten? It can also eat other animals easily. Reproduction doesn't occur until later in life for most animals, (there may be some that can do it instantly, but I wouldn't know). So, if you get eaten, you won't ever reproduce unless you're really lucky. The ones who do survive, will reproduce.
Will you bet that the Cleveland Browns go to the Superbowl? Hopefully not. This is because good teams go. Good teams have good players (traits). They win games (survive). They just don't reproduce.
There is variation in species. There is variation between you an your parents. Who are you to say that traits harmful to ones survival doesn't cause the animal to get killed? And one that helps them to survive doesn't live longer? If I got a trait that gave me immortality, eventually, everyone in the world would have it. The ones that don't will die, and the ones that do won't. (Please don't use my exaggeration as an argument against me. I'm just trying to illustrate the relationship between surviving and reproduction etc.)
The result of this is evolution. Natural Selection explains how it happens. If the idea of design never existed, natural selection would be more of an epiphany than a theory.
Who cares if a creationist came up with the theory? Darwin was a very devout Christian. His findings scared him, and he was unsure of what to think of all of it.
Without natural selection, evolution would not exist.
Think of it this way. Imagine that people used to use coin flipping to settle arguments because thy believed God would choose which side the coin landed on, as a way of settling the debate. Then, someone comes up with the "50-50 theory". He says that the coin will land on one side or the other; that it has a 50% chance to land on either side. Then people freak out and say that if you flip it twice, it can land on heads twice, or that one side is heavier than the other etc. Today, this isn't controversial at all. If it were believed to be controlled by God, I guarantee people would disagree with it, and this question would say "Without chance, where is evidence of 50-50?" "There isn't one case where someone flipped it 100 times, and it alternated between heads and tails."
By the way, I'm hoping you don't think people believe a monkey gave birth to a human. We slowly got these traits, which is why we are so similar. We're similar to all animals in that we have four limbs (two legs, two arms, or two wings), two eyes, two nostrils, one mouth, two ears, major organs, etc. These are important for living. If I was born limbless, and if we still competed to survive, I would not live long enough to pass on some kind of limbless gene (which doesn't exist).
The reason animals don't evolve into having 3 arms (which would be even better than two), is because it's too late for that to happen. We would've had to have had something similar to a 3 arm while we were a lot smaller.
Really doubt you are understanding/accepting this. This answer is for people on the fence, or are willing to open their mind to reason.
Evolution is too slow for me to give an example that you believe, so here is bacteria b/c they don't have as many traits, making noticeable change occur quicker.