Because 'he doesn't want to' and 'he doesn't have to' isn't being debated. If the best justification is because people won't believe him, then that is just as much a LOL rationale as the birthers reasoning for wanting him to show it.
One last crack at explaining this maybe. Pretend you're a birther. You know about the newspaper announcements and live birth certificate and HI public official statements verifying them, and you just don't believe them. You're not convinced. Why the hell would another official HI document convince you where the mountain of evidence before you has failed to do so?
XX: It's coming up again sir, they want more documentation.
BO: Have I not already provided all necessary documentation to establish my citizenship?
XX: You have sir.
BO: And these people who want more, they know about the two newspapers that published announcements of my birth back in 1961?
XX: Yes.
BO: And they've seen the official certificate of live birth issued by Hawaii that is prima facie evidence good in any state or federal court, and state or federal office including the State department?
XX: Yes. But they did think it was fake at first.
BO: But they've since accepted that it's authentic?
XX: Reluctantly, yes.
BO: And they know the Republican governor of Hawaii released an official statement verifying the accuracy of the documents establishing my birth there?
XX: Yes.
BO: And they know the Hawaii Health Dept also issued a statement verifying the authenticity of the documents establishing my birth there?
XX: Yes.
BO: So, I guess my question is...if someone knowing all of the above still doesn't acknowledge that I was born in Hawaii, what exactly is my motivation for releasing any more documents? Would a "long form" birth certificate convince such a person that I was born in Hawaii?
XX: Unlikely.
BO: Would such a person likely contend that any further documentation is either fake or otherwise insufficient to establish my birth in Hawaii?
XX: That is likely.
BO: Would a person holding that view most likely do so because they are opposed to my presidency either due to their opposing political views or because of a racial or ethnic bias?
XX: Those do seem to be the leading correlations among the birther contingent sir.
BO: Then again, I don't see why I should bother to satisfy the demands of crazy, racist, or merely politically motivated people who don't honestly care to see the evidence they are so persistent in asking for and who upon receipt of such evidence wouldn't bother to acknowledge what it tells them anyway.
XX: If you don't they will claim you are hiding something.
BO: Didn't they say that when I produced the newspapers from 1961 announcing my birth?
XX: Well, yes.
BO: Didn't they claim that when I released the original certificate?
XX: Er, yes.
BO: Didn't they say that when I had various members of the press verify the certificate?
XX: Um, yeah.
BO: And when the Hawaii Secretary of Health verified the documents as authentic?
XX: Right.
BO: And when the Republican Governor of Hawaii certified the documents as authentic?
XX: Then too.
BO: And if I went this extra step, bowing to the pressure of bigots and ignoramuses, would they stop asking for anything else? Would it satisfy anyone who isn't already satisfied?
XX: *Sigh*. No sir, they'll just ask for some other documents or won't believe the ones you produce, and they'll still harp on all the other conspiracy theories about dual citizenship or your years in Indonesia or your father's Kenyan ancestry. I think I see sir. I think this is the last time I'll mention this. There's nothing more to be gained from any further disclosure. Good night sir.
Oh, and since this is a thread about Trump, I give you, Louis Black:
http://www.thedailyshow.com/watch/tue-march-22-2011/back-in-black---trump-2012