Of all the theories that science has thrown into the public consciousness, evolution is one of the most obvious and easily understood. Horticulturists and farmers use selective breeding all the time to strengthen their stock, or to select for specific characteristics. It’s not rocket science.
Darwin published The Origin of Species in 1859. It’s not a new idea. It’s not conceptually difficult to understand. Anyone who has parents or children or brothers or sisters can experience it first-hand. After Darwin published his theory, the biologist Thomas Huxley famously declared, “How stupid of me not to have thought of it!”
The precise mechanisms of inheritance – including an understanding of dominant and recessive factors – were meticulously studied by Mendel and presented in 1865.
The detailed workings of DNA and genetics were not uncovered until the 20th century, but the principles of heritability have been well understood by science for 150 years and are entirely non-controversial.
Our evolutionary heritage is clearly preserved in our DNA for all to see. We even have the genes for growing a tail (they are switched off in humans.)
We can see evolution at work in the current human population. For example, people who live at high altitude can have a third more oxygen-carrying red blood cells than those of use who live closer to sea level.
What is the mystery? There is none. One thing holds back public acceptance of science. It is not ignorance. It is not stupidity. It is stubbornness.