well you have not laid out a logical reason why people in Italy would be out to frame this obscure 20 year old college girl.
I think the problem lies with your use of the term "frame".
The contention of many pro-acquittal/pro-innocence commentators (including me) is that no "framing" whatsoever took place - if "framing" is defined as "pursuing a suspect despite knowing that (s)he is innocent, on the basis of some sort of prior prejudice".
Instead, the contention is as follows: in the immediate aftermath of the murder, the local police and prosecutors were incredibly keen to be competent and speedy - and to be SEEN to be competent and speedy - in solving this international-profile grisly murder. They were keen for three main reasons: 1) personal pride and reputation enhancement; 2) they knew the world was watching them, and were desperately keen to show that Perugia could sort this thing out quickly and efficiently; 3) they had bungled very badly in a very similar - but much lower-profile - murder almost exactly a year earlier, and were therefore desperate to show that they had "learned their lesson".
With all this in mind, the police and prosecutors quickly snatched at theory of the crime, based seemingly on Knox's "unorthodox" behaviour after the murder, and the indisputable fact that Knox and Sollecito had, by their own admissions, been in and around the cottage on their own on the morning after the murder. I believe that by the 3rd November, they had decided amongst themselves that they had "solved the crime". I think they decided that Knox definitely knew far more than she was telling them, and that she was very probably involved at some level. I think they thought that Sollecito was covering for her out of a misguided sense of loyalty, but that he possibly wasn't directly involved himself.
And when they found that Knox had exchanged text messages with someone on the night of the murder, this fed straight into their theory. Why hadn't Knox told them about these text messages? To the police/PM, this could only mean one thing: the text messages were linked to the murder. Were they part of the planning or arrangement?
I think that the police and PM had a definite plan for the night of the 5th/6th of November, by which time I believe they were certain in their own minds that they had figured the big picture out perfectly. I think they planned to get Sollecito in on his own at first, and pressurise him until he finally admitted that he was only covering for Knox. I think this would have been the cue for the "lights and sirens" squad to arrest Knox at Sollecito's apartment (they had high surveillance on Knox and Sollecito, so they'd have known where she was), with some handy media there to record the event.
As it happened, Knox came to the police HQ with Sollecito, so they were denied the spectacle of arresting Knox in public. However, the other part of their scheme went - somewhat - to plan. Sollecito equivocated under pressure that he couldn't be sure whether Knox might have left his apartment that night. Bingo!
The police brought Knox in and confronted her with this "abandonment" of her by Sollecito. Bear in mind that they truly thought they were only uncovering the truth here. When they saw the contents of Knox's sent text from the night of the murder - a clumsily-translated "see you later", they took this as further confirmation of their theory: Knox had clearly set a meeting with the recipient of the test message for later that same night.
But who WAS the recipient? Knox could furnish them with the answer to that: Lumumba. Aha! The police surveillance had seen Knox talking with Lumumba outside the university only that very afternoon (the 5th). IN the police's minds this clearly had to have been a covert meeting between the two to check up on the state of the police investigation, and to remind each other not to say or do anything incriminating.
All the pieces of the puzzle had now fallen into place, in the minds of the police and PM: Knox had clearly arranged to meet with Lumumba on the night of the murder. She had indeed left Sollecito's apartment, met with Lumumba, and taken him to the cottage, whereupon Lumumba had sexually assaulted and killed Meredith. Lumumba was the killer; Knox was guilty of assisting the killer and lying to the police; Sollecito was guilty of lying to the police to protect Knox. Case closed!
They went back in to the interrogation room and told Knox they knew exactly what had happened. Knox, they said, had better tell them everything now, in order to protect herself against both Lumumba and the prospect of a far heavier prison sentence. She MUST REMEMBER now what happened, and tell the police and PM everything. Knox said she couldn't remember anything - that all she remembered was being at Sollecito's all night. "NONSENSE!", the police responded. "We KNOW you were there, and we know Lumumba killed Meredith. Tell us the truth!"
And after half an hour or so of this, Knox broke down and told them that perhaps, yes, she could imagine having met with Lumumba and gone with him to the cottage, where he killed Meredith as she cowered in the kitchen covering her ears.
Cue mutual back-slapping thoughout the police HQ. Call in the PM! We've confirmed our theory! They've all confessed! Case closed! All within five days of the murder! Our reputations are assured!
And the rest, as they say, is history. The police and PM called an extraordinary triumphalist press conference the following morning (the 6th) at which they announced to the watching world that they had indeed "solved the case". Incredibly, Perugia Police Chief Artur De Felice inadvertently confirmed exactly what had happened the previous night, when he stated that Knox had initially given a version of events that the police "knew to be incorrect", but that then she finally "bucked" and gave an account of events that "the police knew to be correct".
As soon as that press conference was over, the police and PM were always going to find it extremely hard to change their theory: they had, after all, "solved the crime" - how could they now say "Um, that first time we said we'd solved the crime wasn't quite correct - we've got a new theory, and NOW we've solved the crime!" But three things made it essentially impossible for the theory to be changed:
First, Lumumba was ruled out of the crime. This would have been a huge blow to the police and PM who had so confidently announced "case closed" to the world's media just days earlier. Oops.
Second, forensic results came back, and clearly implicated an entirely different man - Guede - who had not featured at all in the "case closed" triumphalism.
Thirdly, the PM was (and is) a stubborn, arrogant, hubris-filled man. He wasn't going to admit to having got things so badly wrong on the 6th November, if he could avoid it.
So an easy get-out was constructed: why not just substitute Guede for Lumumba in our theory of the crime? That way, we get to preserve the theory in many ways, and we can just blame Knox for misdirecting us to Lumumba.
And that, in a very large nutshell(!), is how and why - in my belief - the police and PM became fixated on pursuing the prosecution of Knox and Sollecito, long after it became obvious that one man (Guede) acting alone had committed the crime.
