There are a lot of reasons that I would disbelieve Evolution...
To start, the new cosmology (Big Bang and it's accompanying theoretical underpinning in general relativity) points to a definite beginning of the universe. This is extremely antimaterialistic. You can invoke neither time nor space nor matter, energy or the laws of nature to explain the origin of the universe. General relativity points to the need for a cause that transcends those domains; namely, God.
Next, Id say 'anthropic fine-tuning'. This means, basically, the fundamental laws and parameters of physics and our universe have precise numerical values that could have been otherwise. That is, there's no fundamental reason for these values to be the way they are. Take universe expansion. Fine-tuned to one part in a trillion trillion trillion trillion trillion. This means, if it were changed by one part in either direction (slower or faster) we could not have a universe capable of sustaining life; so says Stephen Hawking. Fred Hoyle said, 'A commonsense interpretation of the facts suggests that a superintellilect has monkeyed with the physics, as well as chemistry and biology, and there are no blind forces worth speaking about in nature.'
Perhaps it looks fine-tuned because it is?
Next, I would say the origin of life, and the origin of information necessary to bring life into existence, is an argument for the sake of theism. Life at all points requires information, which is stored in DNA and protein molecules in substantial amounts. Here, an idea for an Intelligent Creator isn't what is thought of as an 'argument from ignorance'. This infers design because all other theories fail at this point (natural evolution, etc.) and, the only possible creator of such substantial information at the point of origin for all known things is God.
Then, there's the evidence for design in molecular machines that defy explanation by natural selection. These integrative, complex systems in biological organisms (called 'irreducibly complex') include signal transduction circuits, sophisticated motors and all kinds of biological/chemical circuitry. All of these biological machines need all of their various parts in order to function, but how could it ever be built by a process of natural selection/evolution, acting on random variations? Evolution only preserves things that perform a function. In other words, they preserve things that help the organism to survive to the next generation.
The problem is, these micro-motors perform nothing unless all parts are present and working together in close coordination with each other. Evolution couldn't build a system like this, it can only preserve them, and it's virtually impossible for evolution to take such a huge leap and create the entire system as a whole.
I personally would see these biological systems as evidence for Intelligent Creation, seeing as every time we see such an 'irreducibly complex' system now, an intelligent being is behind it.
More evidence biologically, the Cambrian Explosion is another example. This biological big bang happened during a trivial amount of time (geologically, anyway). Here, around 35 completely unique body plans (skeletal structures) came into existence. You have a huge jump in complexity; it's sudden, and there are no transitional intermediates, no fossils to explain this sudden gap. In normal experience, information is the result of conscious activity, and here we have the geologically sudden explosion of massive amounts of biological data (needed for these body plans), far beyond what evolution can produce.
Finally, Id say human consciousness would definitely support theism. We're not a computer made of meat. We have the capacity for self-reflection, representational art, language, creativity...science can't account for this kind of consciousness coming merely from physical matter interacting in the brain. Where did it come from?