If he admits it, he has no chance of getting out now because his denial has gone on for too long and ANY public sympathy he might have had - hell lose most of it. The campaign keeps him busy and there is always a chance he might just find something that will open his cell. He would also lose any rights to any compensation so IF he did manage to make parole - he'd be penniless.
If he admits it now in order to try to get paroled then what?
He would have to convince a parole board he is truly sorry and regrets his actions, recognizes his actions were wrong and takes responsibility for his actions.
In light of his vehement denials is he likely to be able to convince the of such? No
Does he have much of a chance of getting out if he keeps up his denails? Not really but in his mind he sees more hope and chance in this than he does in getting pareoled for admitting the truth.
He likes attention not only in the press but letters and things to keep him busy and cares about his image to the extent that if he admits guilt then he will go down in hisotry as for sure a murderer as opposed to one who maintained innocence and all those writing and giving him attention will stop doing so.
So either way he will not get out but he has more to lose in the form of people who pay attention to him and give him something to do and he likes having the hope he could get out one day.
People like his sometimes confess on their deathbed for the sake of relatives of victims and they no longer have to worry about what supporters think but i don't even see any of that applying here.
I even think he has tried to convince himself he is innocent and didn't do it and tries to block out what really happened.
I see a greater chance of hell freezing over than him ever confessing.