Well, there are a few answers to that question. The first is, because I can. The second, and more important answer is, I can use the transformer for all manner of OTHER projects. For example, you could wire up a couple of these bad boys together and make a welding machine. Or, you could do what I intend to do, which is to make an electrochemical etching machine for putting my maker's mark on the knives I make and sell.
So... without further ado, let's jump right into this. But first, a couple of comments. For this Instructable, I will assume you know how to take apart a microwave oven. Ideally for what we want, you want an older oven, one that uses a big transformer - the bigger the better, really. Why? Because bigger (and older, to a point) typically means both more power and higher quality. Ideally, you want to find one of those old Japanese or American microwaves from the late 70s, 80s, or even early 90s.
Also, keep in mind that you are working with high energy electronic parts. Keep that in mind. Make sure everything is unplugged from a power source, and ensure that you are working in a well-lit, safe, clean workspace. I tend to do a lot of my work like this at my local Techshop, which is where I actually completed this task.