Not all transgendered people want to surgically transition! The feeling of hatred or wrongness about your own body is called "dysphoria" and in different transpeople this level of dysphoria can be different. Some people know they are transgender but don't feel any particular discomfort toward their own bodies and may be content with being respected as their internal gender (through pronoun/name changes, or appearance changes such as clothing, hair style etc) without feeling the need to radically change what they were born with. Others despise their external shell so much they'll do anything to make it "right".

Perhaps it might be worth thinking about it in a "magic button" way... If you could press a magic button that would change your body, would you do it? No surgery involved, just magic. Some trans people would change their bodies if it were possible to do so, but are afraid of surgery, or have a fear of disappointment with the end result, can't afford it, or any number of reasons.

As I've said before, transgender =/= transsexual. Anyone who has a different mental gender to their physical sex is transgender, but a transsexual is someone who is, wants to, intends to or has physically transitioned. Not all transsexuals successfully complete the transition.

~Edit- http://forums.psychcentral.com/showthread.php?t=224745 This big load of waffle that I wrote a while ago might explain dysphoria and transitioning a bit better...