Well I suppose thats why I have so little faith in evolution when it comes to crossing phyla. There is too much misinformation during school when it is taught. Information that makes it look like one thing, when in reality it is something totally different. Mutations and natural selection were taught as 2 entirely different things in my school. Sure they would occasionally work together, however, the prime way evolution was taught, we will take darwins finches as just an example, was that things such as beaks growing larger, had nothing to do with mutations, and were just a natural process. And this process was considered to be the main driving force for evolution.
Unless of course, Im misunderstanding you, and that IS how it works.
Your school must have had bad teachers. What you described is known as Lamarckian evolution, after its proponent Jean-Baptiste Lamarck. He believed that animals would adapt to their environments in their own lifetimes (like giraffes growing larger necks to reach taller trees) and pass that genetics onto their children. Darwin's theory of evolution, which has achieved scientific consensus, was that organisms would have children with slightly different genetics (due to mutations or sexual reproduction or in some bacteria lateral genetic transfer), and if that resulted in a benefit to reproduction it would in turn be passed down to their children.
Basically, evolution has three main requirements. If satisfied, it is a mathematical certainty that the system will evolve; biological evolution is just a specific case of a more general feedback system rule, albeit an extremely elegant one.
1. Entities must reproduce themselves - Reproduction.
2. Variation must be introduced over generations - Variation.
3. The chance of reproduction must be dependent on which variations do or do not occur - Selection.
If all three conditions (reproduction, variation and selection) are satisfied, evolution occurs. The converse is also true; a system without reproduction, variation or selection will not evolve in an optimisation sense. The debate over intelligent design and evolution doesn't usually dispute this; it's usually focussed more on whether these variations are capable of producing the diversity of life we see today (I assume you agree, based on your last post).
We have two types of reproduction: sexual and asexual. Sexual reproduction involves a recombination of two parent's chromosomes, while asexual reproduction is basically cloning (different mechanisms for it that we don't need to go into here). We also have three types of variation: mutation, recombination and lateral transfer. Mutation creates novel genes, recombination creates novel combinations of genes, and lateral transfer puts old genes in new genetic environments (genomes). For the purposes of evolution, mutation is more 'powerful' than recombination, which is more 'powerful' than lateral transfer (mainly because lateral transfer allows viruses to inject RNA and other badness), but all are still important.
It is (or should be) beyond dispute that an idealised series of mutations could result in any organism on earth. It is trivial to show that a very long series of insertions, deletions and swaps could create any DNA string starting from any other. And that's all a mutation is: one or more insertions, deletions or swaps. Now not every pathway would create organisms that would survive to reproduce even in ideal conditions, and some mutations would be removed by natural selection - it takes energy to replicate DNA, and shorter sequences are ever so slightly better. A long, pointless stretch of DNA (like junk DNA in humans and other animals, but much more of it) would be selected against. So I'm not saying that it is indisputable that macro-evolution occurs. The science is conclusive that it does, but I at least have the intellectual honesty to acknowledge that there are objections. Whether or not the objections are valid is another matter.