I've done a lot of coding of one kind or another over the years. And my impression is that an essentially random set variations or mutations in a complex binary code would result in system failure far more often than in positive traits that would then presumably be passed on if the individual reproduced successfully.
And then we have complex multi-cellular forms in competition with pathogenic asexual single cell forms which are able to mutate far more quickly. And yet, so far at least, no single sell form has succeeded in wiping out other forms entirely. That really shouldn't be all that difficult either. In other words, with the incentive simple life has to fill the world with it own form, and given that bacteria for instance can mutate so very fast, why has no bacterium ever eliminated all the competition?
But a the same time, nature supposedly has created a far more cumbersome and fragile species in the form of humans, that mutates much more slowly than any germ, but seems to be on the cusp of the ultimate power of eliminating all competitive forms.
That is of course, not terribly mathematical reasoning, and descends largely from my own impressions. But it still seems to me that evolution in and of itself is inadequate to the type, variety and interdependence found in modern life. People often state "how old" life in Earth is. But really it isn't all that old, even if you allow one non-fatal gene mutation per species per day that is then passed on successfully, and this is before we even consider whether the mutations described impart any improved chance of survival. Three billion years times three hundred and sixty five and a quarter days, it is still a manageable number, and represents far fewer mutations than I expect would be required to produce such an organized system.
I'm not articulating this terribly well, but better authors than I have.
I do think that we well might suffer from a common fallacy. To illustrate, if we were all intelligent insects, and we'd arisen from our eggs and cocoons in a well manicured family garden during the two week that the family was away on vacation, we might well come to the conclusion that the trimmed hedges and rows of flowers had all occurred just as they were by purely natural causes, because we'd never seen humans planting and trimming.
So, I have little trouble accepting evolution per se, but I do believe that other agents are at work.