It seems to me that turning a pole into a hole involves chopping off the pole, I am no doctor though, so I suppose I can't say for sure. Regardless of how it is done, it is clearly a very extreme mutilation, much more so than piercings, scarification or even boob jobs.In the case of amputation, you are losing the functionality of your limb.
In the case of a sex change, nothing is actually being "cut off." Existing tissue is being restructured so it's a hole instead of a pole (or in rare cases, vice versa). No functionality is lost; the patient is still able to urinate and have sex. They won't ever be able to reproduce, but lots of people get surgery to eliminate that functionality anyway.
It seems to me that Jamesrage's analogy is right on track. What fundamental difference is there between someone who thinks they are a woman trapped in a man's body and someone who thinks they are a duck trapped in a man's body?
Certainly the man might claim to be happier after feathers have been grafted into his skin, but I can't help but wonder about the moral fiber of a doctor who grafts duck feathers into a man's skin to help him feel more like a duck.