I too have read many books which indicate that the evolution of species does in fact occur. I certainly do not claim that one species cannot evolve into another. The fact is, I have not observed any species evolving into another species. That is not to say that I believe an evolution of species does not take place. It means that I am not certain that it does take place.
What do you mean by "certain"?
Few things are 100% certain (generally only by definition), but we can have
reasonable certainty about the theory of evolution, because nothing else better explains or predicts all of the relevant evidence and does not contradict that evidence.
Perhaps at the root of my problem with evolution is that scientists have set up a classification system which very narrowly defines what each particular species is,
This isn't exactly accurate. The classification system is to help us understand the relationship between individual groups of lifeforms. Taxonomists don't "define" what a species is, the characteristics of the lifeforms are what define what species they are. The name for some species have changed as scientists discovered that the species was actually related to a different group than was originally thought.
Calling something a "species" is merely a label given by humans to help categorize what they've found into groups and sub-groups using a method which is as unbiased as possible. As one species evolves into another there is no hard line between one and the other. It's very fuzzy and gradual, and it's actually somewhat arbitrary where they are grouped, often based on what it looked like when the original fossils were found or some similar point in the history of that branch of its evolution.
which on the one hand I believe is a very good system for precisely distinguishing one creature from another according to specific physical characteristics and traits, but seemingly fails in my opinion because a species does not truly evolve into another species over time.
"Truly evolve"? I think you misunderstand evolution here.
A species does not change into another species over time. It is the characteristics and traits of a species that changes.
The frequency of characteristics and traits changing in a species over time is
exactly what evolution is. If each generation gets a tiny bit more different from some particular generation in the past over many generations, then after a while the current generation will be different enough to be described as a different species from that other particular generation. That's a perfect example of something "truly evolving".
What you're describing is how evolution says things work, you just don't seem to understand that this is
indeed true evolution.
Thus, according to the present classification system, if a species were to undergo significant changes over time, those changes would indicate that a new species has come into existence.
And you're essentially correct, though you say "come into existence" as though something happened suddenly with some clear demarcation, when it's actually gradual, fuzzy, and, to a certain degree, arbitrary.
But the fact is that evolution does not involve a changing of one species into another species. It is still the same species, but the characteristics of that species changes over time.
If the species now has many consistently different characteristics from the much earlier species, how is it "still the same species"?!? It may have many of the same or similar characteristics to its distant ancestor species, but once enough changes have accumulated over many generations, calling that much different species "the same species" as its distant ancestors is just silly.
If you have a hammer, and the head of the hammer breaks, so you replace the head of the hammer, then the handle breaks, and you replace the handle, is that "the same hammer" to you too? They are related, but not the same.
The Bible fully supports the concept that the evolution of species does take place. There are no contradictions between the Bible and accurate science.
LOL. OK, that's a bridge too far. "No contradictions," eh? Galileo was persecuted because he showed using science that the Earth isn't the center of the universe, which contradicts the Bible. Claiming that a book which claims that the world was created in six days, life appeared fully formed, with trees existing before the sun, and man being formed from clay and woman coming from his rib (to name just a few examples) doesn't contradict actual science requires some rather deep levels of denial. Heck, the Bible even contradicts
itself on the order that life appeared. Genesis 1:20-23 says that fish and birds were created on day 5, then other animals and finally man on day 6 in Genesis 1:24-31. On the other hand, Genesis 2:4-7 has man created first, then all other animals created next as helpers for man in Genesis 2:18-20.
If the Bible can't consistently say whether man came first or last among animals which were supposedly created by God, I have guess that you never even bothered to test your claim that, "There are no contradictions between the Bible and accurate science," you simply believed it because you wanted it to be true.
Care to rethink that claim?