Re: electron spin
Your question is a bit like asking why electrons exhibit a gravitational field. Spin is just a fundamental property that electrons (and some nuclei) have.
Further to the comment from the previous posters, electrons don't actually spin in the sense that they're little round balls twisting on an axis. However, they show all the behavior you would expect from little spinning balls - they do have angular momentum (this is the principle behind electron spin resonance). However, because we're now in a quantum world, both spin and angular momentum are quantized, meaning that they can only have certain discrete values.