Let's just examine this train of thought shall we?
Imagine for one minute you are innocent despite the pronouncements of whichever part of the legal system you're caught up in. You've had to play a game for years, learning "rules" that seem illogical and non-sensical. By which I mean your legal experts, who are not also medical experts and dependent on outsourcing to a small number of specialists, have advised you to not say or do any number of things you feel are relevant because in the past certain things have seemed to negatively impact the outcome of similar cases - for example, you find an expert who has worked on a number of similar cases to your own and due to their knowledge and expertise have pretty robust alternative explanations to that of the prosecution. However, despite their qualifications and expertise they are considered a maverick or outlier because they go against entrenched dogma that has been repeated so often in courts, and won many prosecutions, so asking the court for permission to use them is off the table because it would prejudice the case against you by simply uttering their name in legal circles. That's one part of the game. Truth is actually sacrificed early on to protocol.
The fear is that guilty people will get off if the alternative view gains traction. The logic is that there are far more guilty people than innocent, so if a few innocents slip through the net when it comes to public safety and particularly in cases regarding children, those outlying innocents are worthy collateral damage, and should martyr themselves for the greater good.
There are a few tactics employed to bring a recalcitrant and apparently guilty but innocent in their own mind / knowledge defendents to heal.
One is to keep hammering away at them to respect the system, and the process, and the experts, because you are nothing in comparison. Challenging it is supremely arrogant, because while miscarriages of justice do happen, it's very rare. Which up until you're on the receiving end, you have previously believed (naively). You have been up to this point, generally law abiding, have had respect for the system and believed that telling the truth is your saving grace. So you tell your truth, and everyone opposing you, because that is their job, says "Nope. You're lying. Our expertise outweighs your belief in your innocence. And our reputations are on the line if we, at this point, in the public arena, change our stance. Accept your guilt." One term for this is institutional gas-lighting.
Then there are the appeals to your better nature - the one you obviously don't have because you're a child abuservir killer. There are long conversations with professionals who point out how traumatic it is for the people who are essentially victimising you to have to do so. They want this to be over for everyone's sake. They are losing sleep and under stress because you won't admit your obvious guilt - obvious to everyone but you, because you were there, you know you didn't do it.
So because you're a tough nut to crack, the psychologists come in. They are even more uneasy and uncomfortable in some cases. They find you challenging, you don't have a diagnosable condition to explain your aberration behaviour. There are a few pink flags, potentially - you come from a broken home, one of your parents had a mental breakdown in your childhood, but your school record is good, you've never been in trouble with the law, you are not an addict or an alcoholic. You have loved and well cared for pets. Your biggest "symptom" is doggedly maintaining your innocence and bringing your research to experts who don't want to see it. In the courts eyes, this makes you even worse. You have no mitigating factors to provide a reason for your heinous acts.
And the cost. The extravagant waste of public money. Oh yes. This can't go on for ever. You are by pursuing your innocence, taking money from the public purse, and putting vulnerable children at risk, tying up professionals with better things to do with all your nonsense of proclaiming innocence. If you had a shred of decency you'd just confess and let everyone go back to their lives.
In criminal court, a confession can make prison life less onerous. The authorities will make concessions. Maintaining your innocence gets you a much rougher ride. Hence false confessions and admissions of guilt. When an innocent person has confessed, and is then exonerated, people are baffled. "If you are innocent, why did you do that?" some will ask, usually those with no direct knowledge or experience of such legal proceedings. The answer is because they took legal advice. They were ground down to the point where they had actually started to doubt their innocence through the subtle brainwashing employed by the raft of people telling them, for a fact, they were guilty, and also telling everyone around them, including a jury.
There is of course the appeals process, and the CCRC. So all is not necessarily lost. But that depends on having a legal team ongoing that you can work with closely enough while navigating and trying to survive in the prison system which is obviously designed to punish you and remind you every day that you are guilty, even if you're not.
I ask you, if you were in this situation, how far do you think you'd go to prove your innocence in the face of all that? Knowing that to all intents and purposes you were potentially pissing in the wind ? Realising that every time you brought up a detail that might be relevant your legal team and the authorities were essentially rolling their eyes at your naivety and may have got to the point of wishing you'd just shut up and get over it?
In my own case, I had to back down or lose my child to adoption. There are many versions of this hell you see.