I am opposed to materialist explanations of our origins: e.g. the notion that life came from non-life, or intelligence came from non-intelligence.
And Darwin most certainly did teach that simple life forms became complex life forms via random mutation plus survival. As such, Darwin taught that life was able to cross every taxonomic boundary, from the simplest proto-cells, all the way to mankind, and without a shred of evidence beyond minor variations within species.
And finally, shared DNA between diverse organisms is much better explained by common design than common descent. Indeed, one would think that any shared DNA between organisms that are supposedly separated by so many millions of years would have long since been obliterated if evolution was true.
Why? Aren't living things made out of material, and didn't God create material? It's not like we've discovered magic pixie dust is the building block of living things.
You can dispose of Darwin's supposedly flawed theories in quick order; simply propose a better explanation.
Admittedly, life from non-life is a tough nut to explain. That's why most people, (including Darwin), don't bother trying. I haven't tried to explain it myself, except to imply that time has a tremendous multiplier effect.
Intelligence from non-intelligence is not as mysterious. You can observe living organisms, ranging from ourselves down to paramecia and bacteria, and see that each organism uses a variety of survival strategies. Reaction to stimulus and the possession of rudimentary memory skills would easily seem to be the harbingers of a developing intelligence.
But assuming that intelligence did develop on its own somehow, it certainly took a very long time in doing so, including the tremendously long period which is called the reign of the dinosaurs.
Various scenarios suggest the dinosaurs were the top of the food chain for more than 300 million years. In comparison to our supposedly having risen from proto-mammalian ancestors after the dinosaurs died sixty-five million years ago, dinosaurs clearly had ample time to develop languages and culture if it was an easy thing to do. They didn't.
But perhaps they were the "giants" on whose backs we now stand for our more lofty perspective. They "explored" every other biological manifestation they could get their scaly claws on.
Maybe it just took a long, long time.
"... that simple life forms became complex life forms via random mutation plus survival."
You leave out a lot when you simplify it so drastically. Genetic survival depends not only on the occasional random mutation, but on the shuffling and redistribution process of the genes in every generation. It isn't just mutation, it's also sex, if that isn't too distateful a way to put it.
Oftentimes, extra material is included, at no harm or relative cost to the individual. This material is as handy as a pocket on a shirt, allowing animals to develop new capabilities gradually, instead of all at once. This can be presumed to be the explanation for how some animals see color with two color receptors in their eyes, while other animals have three color receptors for an even richer world of color. Many have four!
With extra material in the genome, random mutation affecting that material would not do harm to the animal or its offspring, and may eventually prove to be beneficial. Obviously, it's a gradual process. (Equally obviously, it doesn't happen with just a single fortuitous mutation.)
"And finally, shared DNA between diverse organisms is much better explained by common design than common descent."
I don't see why either explanation is preferable over the other. What I see is that common descent would have clearly delineated markings of time on its operations. Over time, the magnificent detail and coloration of this tapestry of genetic invention would become tattered and worn, as various bits of extraneous but not lethal, or perhaps even beneficial material came to replace the original pattern.
This is what we observe with our study. From geological strata of known antiquity come shapes of ancient origin, with their unique and distinctive patterns of creation, while modern animals and people have discernible differences in shape, chemical operations, and in the pattern of their genes that specifies how they are to make themselves fit their world.
If they were all independently developed to fit their ecological niches by an "unrelated" process, then they would be as dissimilar from each other as books in a library, instead of showing the gradual modification that we see in such phenomena as languages.
When you read the Canterbury Tales, you know that you are reading "English", but you also know that something is a bit different about it. Time changes things. Time changes everything.