I believe that the processes and psychology driving the actions of Mignini and the State Police during November/December 2007 can all be reasonably explained with reference to the following propositions, with my suggested inferences alongside each one:
1) Mignini and the police were in the truly international spotlight from November 2nd onwards, with the whole of Perugia in uproar, the prospect of hoards of students deserting the city in panic, and the world's media rolling into town; IMO this made Mignini and the police extremely eager to be seen to be competent "super sleuths", solving the crime in quick time and basking in the glory of their achievements in doing so.
2) Mignini (and a small subsection of the police in this case) had previously found themselves in the national (and lower-key international) spotlight in respect of the Monster of Florence case - and Mignini in particular had suffered professional (and some personal) humiliation over his handling of that case; IMO this made Mignini determined to show everyone that his handling of the Kercher case.
3) The Perugia prosecutors and police had dismally failed to solve what had, in fact, almost certainly been a straightforward murder case almost exactly a year previously, when an Italian female student had been killed: the PM and police abjectly failed to investigate the woman's boyfriend properly or collect evidence in a timely/professional fashion, when he almost certainly was the culprit; IMO this also fed into the desire/need to solve the Kercher murder quickly, professionally and brilliantly.
4) I think Mignini and Giobbi in particular thought of themselves as highly intuitive sleuths, who could figure out crimes by connecting abstract pieces of "evidence" and the behaviours of potential suspects; IMO this was a crucially important factor in the way that they decided so early on (in the total absence of any proper evidence, of course) that Knox in particular was heavily involved in the murder.
5) I believe that Mignini and the police had a well-practised system for "solving" crimes, which they employed in the Kercher case: they intuitively figured out who the culprits were, they brought the culprits in - without formally declaring them a suspect - and extracted a confession from them*, they then tried to get a trial-admissible confession by engineering a "spontaneous declaration" to the PM, and they then went searching for physical evidence to bolster their case; I'm sure that they'd secured many legitimate convictions using this method, and in Italy's unfit-for-purpose justice system where courts still acted in a quasi-inquisitorial manner where prosecutors were impartial "truth seekers" and it was effectively the defence's job to disprove the prosecution case, this would have been a highly effective method.
So what do I think most probably happened in this case? Well, I genuinely believe that Mignini and Giobbi sincerely thought they'd correctly identified Knox as a prime culprit in the Kercher murder. I think they thought Knox had met up with another man (at what precise point they concluded that this other man was Lumumba is still unclear, but the evidence shows it was at least most definitely before Knox made her first "confession/accusation") and had taken him to the cottage to assault and kill Kercher. I think that prior to 5th November, they were unclear as to Sollecito's role: he was either innocent of participation in the murder but lying about Knox's whereabouts to protect her, or he was a co-perpetrator and was lying to protect both himself and Knox.
I think that the PM and police carefully orchestrated a plan for the evening of 5th/6th November. The original plan was a multi-staged approach. They knew (from surveillance and other means) that Knox was staying in Sollecito's apartment. Firstly they would bring Sollecito in on his own and extract from him, at the very least, a confession that he'd been lying about Knox being with him in his apartment throughout all the evening/night of the murder.
This would obviously give the police/PM ample probable cause to send the cavalcade into town (probably having tipped off the media before hand so they'd be there to witness everything) to arrest Knox and take her back to the police HQ. And once confronted with Sollecito's confession and the force of authority of the police interrogators, Knox herself would "buckle" in turn and confess to her participation in the murder, as well as naming the "third man". The police would then go and pick Lumumba up (they knew he lived a long way from Knox and it was the middle of the night, so there'd be almost no chance that he'd have even been aware of Knox's arrest).
And having extracted these confessions (coupled with "spontaneous declarations" which they hoped to be able to use in court), the PM and police would simply dot the i's and cross the t's by collecting a bunch of evidence to bolster their case in court. After all, they'd correctly solved the crime, so almost by definition there would be supporting physical evidence and witness evidence pointing towards the culprits. In their minds, the confessions (or, more accurately, "confessions") simply served to prove their Holmes-esque hunches. They were geniuses. They'd solved the crime and put the culprits behind bars pending further investigation and the inevitable charges, and all within just over five days of the murder itself. The triumphalist press conference on the morning of 6th November is an important indicator of the mindset and motivation of the PM and senior police in this case. As, of course, were the ill-judged words to a group of journalists spoken by Perugia police chief De Felice (clearly pumped up with hubris and excitement), who served to provide extremely strong evidence that the PM/police had indeed already decided that at least Knox was involved in the murder (and that Sollecito was at least guilty of a serious criminal offence) BEFORE they were brought in for interrogation the previous night: he indicated explicitly that the authorities "knew" that Knox/Sollecito were lying, but that the interrogators successfully made them "buckle" and tell them "the truth".....
And we know for sure (from various testimony and evidence) that the PM and police employed highly suspect-centric methods in the ways in which they collected/analysed physical evidence and witness statements. Everything which supported their a priori conclusion was accepted near-automatically as reliable and credible, and anything contradicting their case was discarded. So when they seized Sollecito's kitchen knife, then instructed Stefanoni to find incriminating evidence on it, and then Stefanoni (owing to contamination and/or malpractice at some point in the chain of evidence and her own improper lab methods/protocols) "found" Kercher's DNA on the knife, the PM and police concluded the Sollecito must have played a more active part in the murder. This shift in view was further bolstered by evidence in respect of Sollecito's mobile phone: the police misinterpreted (possibly wilfully) the signal dropout of Sollecito's phone that evening to infer that Sollecito had actively turned off his mobile at around the time of the murder - and why would Sollecito have done that unless he too was an active participant....?
So Mignini and the police thought this one was totally in the bag, that corroborating evidence would clearly be forthcoming, that the convictions in court would be a slam-dunk, and that their (Mignini and the senior police) reputations would be gilded and elevated by their brilliance in the way they'd solved this case.
Until
Two things happened: it turned out that Lumumba had a very strong alibi (despite the police's active attempts to frustrate the alibi - and indeed to find a "witness" to state that Lumumba had left his bar at around the time of the murder (when in fact he'd stayed in his bar all that evening), and one of Guede's friends came to them to tell them that Guede had effectively made a form of confession to being at the murder scene (and that Guede had mysteriously fled to Germany).
Now, by this time, I believe that Mignini and the police had huge amounts of professional and personal pride invested in their version of events. To have radically changed their position at that point would IMO have seemed like professional suicide to them. And (improper) physical evidence was starting to come in which apparently cemented the Knox/Sollecito link. What to do? Well, the answer was obvious: the PM and police could effectively maintain their version of events (and thus safeguard their reputations of super-sleuthing in this case) by simply swapping out Lumumba and swapping in Guede - and (darkly brilliantly) blaming the "evil and manipulative" Knox for the initial focus on Lumumba.
All of this only scratches the surface IMO, and it's before we even address the improper and unlawful ways in which the convicting lower courts heard and assessed the evidence and reached their verdicts (mistakes which, fortunately for justice, the Supreme Court was ultimately able to identify and correct). But I've already written a gargantuan post and it's getting late!
* And remember (as I've linked to several times in these threads) the European Criminal Bar Association long ago identified this institutionalised malpractice in Italy of the police/PM deliberately failing to declare as a suspect people whom they actually did view as a suspect, meaning that they could question those people without any access to a lawyer or understanding of their rights, in order to obtain confessions.