William Paley's famous 'watchmaker' analogy is based on a teleological argument. The basis of this is that the universe is too complex to have evolved but must have an intelligence behind it.

The first thing wrong with this is that there is no evidence for it. The more we study, for example, the fossil record, the clearer it becomes that every organism evolved slowly, adapting to changes in its environment. A good example is the eye - it used to be argued that 'there is no such thing as half an eye', eg they can't have evolved by themselves but must have been created - which is now known to have evolved over millions of years from simple light-sensitive organisms.

Another major problem with this argument is: if the universe can't have evolved without a designer, then the designer can't just have appeared either, so who designed him/her/it?

There are plenty of other proofs that this argument is wrong: you can find some of them here.