Four insurmountable reasons
There are four reasons (at least) why I will never (ever) believe in the theory of evolution. These are not problems which might one day be solved by future findings, they are insurmountable infinite problems, which no future knowledge could ever resolve. They are category problems. I present them simply here and hope to expand in the future.
1. The origin of the first cell - or any cell
2. The Cambrian Explosion
Around 550mya (again, if we assume...) there was a sudden explosion of most of the existing categories of life on earth. Before that era life forms were simple, after that complex. Even the evolutionist Stephen Jay Gould recognized this as a pretty big obstacle to the gradualism of evolution.
3. The amazing mind/heart/soul of man
It may be possible to trace a gradual upward incline if we run from amoeba to apes. But then when we come to man we have a sharp discontinuity, infinite in step size. In spite of all the attempts to bring apes up to man and the other attempts to bring man down to apes, the gap remains infinite. The brightest chimps are as "thick as two short planks" compared to mankind. It is nothing short of the blindness imposed by Darwin that enabled National Geographic to bequeath the title about some dumb chimps, "Almost Human". What did they find in the forest? Chimps making fire? Playing musical instruments? Doing Algebra? Painting pictures? No, they found dumb apes doing nothing more than being dumb apes. Don't get me wrong Apes are wonderful creatures, but the difference between them and us is an infinite - and here's the point - and unexplainable (in Darwinian terms) chasm. None of our remarkable, unique powers are necessary or advantageous to survival - the ability to make a decision, for example, rather than to respond instinctively to an event, could be a disastrous disadvantage and result in immediate death.
4. The theory is upheld by naturalism, the most unscientific science ever devised
Most people who believe in evolution also believe in naturalism, the idea that there is no such thing as a God or any such entity and that EVERYTHING can be explained by natural law. Thus, they never consider alternative explanations when they are "in the corner", "against the ropes" or "up a gum tree". Their boxed up minds can only run in the boring old intellect-quenching, imagination-destroying, theory-stopping channel of "it must be natural"; they are unable to think outside this tiny steel box and even imagine that there could be another way to explain the marvels (1-3 above) they see. If that's "science", the sooner it belongs to history, the better. True science is prepared to consider all possibilities in its free spirit of enquiry, including "this required intelligence."
Those committed to methodological naturalism are like the alien atheist who lands on planet earth after the third world war, visits the amazing Rushmore stone carvings and goes to work trying to figure out how the winds (or water) carved the faces of presidents over thousands of years. If you think this is an outrageous or fanciful analogy, you are entirely mistaken. The complexity of the simplest cell is infinitely more complex than any rock carving and yet it is deemed the work of natural forces. A physicist would struggle immensely to come up with a "just so" theory as to how something like Rushmore was formed "naturally" by water or winds, and we're talking exceedingly simple stuff in the case of Rushmore.
These objections are not quantitative doubts which future findings could one day dispel, they are qualitative doubts, which can't by their very nature be explained away. Ever.