This is a deep question - really one of the most fundamental questions biology has. Where do all the myriad animals and plants come from. IMHO its natural that you have these questions because your view is the more intuitive one. In fact it was in some ways the dominant view of biology for over over a thousand years.
I'm going to take a different tack here and hold that the answer why nobody's going to abandon evolution is that there is no coherent theory (creationistic or otherwise) that even comes close to explaining what biologists see.
Science does not simply want to throw away a theory because there are blemishes - in fact there is no such theory in any of science that is complete and perfect and its been proven mathematically. We have to have another theory that is better at explaining what is known and people will migrate to it.
In fact this is what nearly every scientist I know finds so magnetic about the pursuit. Any Joe with a garage lab has a chance (however small!) in finding the next great discovery, of upending the current order of things. It has happened several times in fact. But its also fair to say that it is not so easy.
Its interesting to note that it was fairly recently (19th century) that all educated people assumed that the forms of animals were directly ordained by God - created perfect for the environment in which they found themselves.
In any case, basically this sort of creationism was the dominant theory of all living things (I'm giving it a more modern title, but it seems to fit.). But that did end for most people when they reviewed Darwin's arguments. That theory was found to have several flaws that just could not be ignored and was thrown out as being too imperfect. Evolution is in place because it was found to be more perfect than the previous theory. Anything that follows it will have to do so for anyone who really cares to think about it.
Here is a list of things that Darwin explained so clearly that have not really been explained any other way. Others may fill in the comments to improve this list, but this can get things started:
1) We have seen lots of cases where species appeared from previous ones. Previous to Darwin, animals and plants came directly from the mind of God. The creator would conceive of a perfect animal who would live on an arid mountain and just put them there. This was satisfactory in that you would go from one mountain to another and find pretty much the same goats and plants. But when Darwin performed a survey over most of the world, and in particular in the Galapagos Island, he found different animals to be living identical environments on different islands. This is evolution observed directly- we now understand that islands get new animals very rarely and so a single group of birds can then speciate after they arrive on an island and take up niches (lifestyles) that other animals would have in europe say. Darwins' finches who eat different kinds of bugs are a good example of cases where its clear new species just popped up because there was time enough and food enough for them to do so. Islands have lots of other more obvious cases. The big birds of the south pacific, the moa could reach 12 feet high and didn't even have wings. They ate plants and could run like the dickens - its basically a deer. Where did these species come from, if not from others which landed on the island and turned into monsters and midget birds?
2) The theory of natural selection and evolution pretty much predicted the discovery of DNA and allowed the rigorous relationship between all living things on earth to be established. The discovery of DNA illustrates that all living things are almost related to each other. They share the same genes, the older families of genes are the most widely found amongst not only animals, but also plants fungi and bacteria. If there were no evolutionary tree where species radiated from common ancestors why do different species relate to each other so clearly ? No one who looks at the DNA sequences would question that we are related to yeast just as surely as a paternity test shows a father and son are related. I see no great outcry against genetic paternity tests, but they use the same argument.
No, nobody who really cares about knowledge is just going to forget about evolution.
I may add more here, but this is getting long.
Just to go further into some of your examples though:
'I can't change my DNA if I want to get taller'.
Not yet, because we are still learning. Gene therapy treatments that are being worked on change the DNA of your cells to get rid of diabetes, cancer, hemophilia and others. There is biological treatment for some dwarfism. The very complicated genetic factors that determine your height are poorly understood, but in principle it could happen. I am average height and I don't really want to be taller - not sure why this particular problem deserves a lot of interest.
