As I understood his question, the strangeness is not the inclusion of this material, but rather its placement. Why at this moment in the journey, when one would think that mind, heart and soul would be reaching a point of ardor, turning to a sublime apprehension that will eclipse the Earth, let alone one city?
Florence is Dante's patria -- the body politic, the seed plot of the poet's broken earthly life. For some reason, he now has to turn and look close up at it with Cacciaguida, the radice, root of his life. Why?
It's a rich portrait, with much to ponder. Dante tells a story that has remarkable elements. Florence begins imagined as a modest young woman, and after the catalog of famous families, the tale culminates in the tale of the betrayal of a modest young woman.
Why does Dante make the murder of Buondelmonti the climactic moment of his narrative? Here's the tale as told in a chronicle attributed appropriately enough to a "pseudo Brunetto Latini":
In the year 1216, when Messer Currado Orlandi was podestà, Messer Mazzingo Tegrimi of the family Mazzinghi had himself knighted at a place called Campi, some six miles from Florence, and invited there all the best people [tutta la buona gente] of the town.
When all the knights had sat down to meat, a buffoon snatched away the full plate set before Messer Uberto dell’Infangati, who was paired at table with Messer Buondelmonte de’ Buondelmonti. This angered Messer Uberto greatly, and Messer Oddo Arrighi de’ Fifanti, a man of valor, roughly reproved him on this account. In reply Messer Uberto told him he lied in his throat, at which Messer Arrighi tossed a full plate in his face. The whole assembly was in an uproar. When the tables had been removed, Messer Buondelmonte struck Messer Oddo Arrighi with a knife and wounded him severely.
As soon as all the company had returned to their homes, Messer Oddo Arrighi took counsel with his friends and relatives, among whom were the counts of Gangalandi, the Uberti, the Lamberti and the Amidei. Their advice was that peace should be concluded over the matter, as a sign of which Messer Buondelmonte should take for wife the daughter of Messer Lambertuccio de’ Amidei, who lived at the head of the bridge. The bride-to-be was the niece of Messer Oddo Arrighi. Accordingly the marriage contract was drawn up and the peace arranged; on the following day the wedding was to be celebrated.
Then Madonna Gualdrada, wife of Messer Forese Donati, sent secretly for Messer Buondelmonte and when he came spoke to him as follows: “Knight, you are forever disgraced by taking a wife out of fear of the Uberti and the Fifanti; leave her you have taken and take this other [i.e. her own daughter] and your honor as knight will be restored.”
As soon as he had heard, he resolved to do as he was told without taking counsel with any of his kin. And when on the following day, the morning of Thursday February 11, the guests of both parties had assembled, Messer Buondelmonte passed through the gate of Santa Maria and went to pledge his troth with the girl of the Donati family, and left the Amidei girl waiting at the church door.
This insult enraged Messer Oddo Arrighi greatly and he held a meeting with all his friends and relatives in the church of Santa Maria sopra Porta. When all were assembled he complained in strong terms of the disgrace put upon him by Messer Buondelmonte. Some counseled that Buondelmonte be given a beating, others that he be wounded in the face. At this spoke up Messer Mosca de’ Lamberti: “Whoever beats or wounds him, let him first see that his own grave has been dug; a thing done has its own head [cosa fatta capo ha].” They then decided that the vendetta was to be carried out at the very place where the injury had been done, when the parties had gathered for the exchange of the marriage vows.
|Murder of Buondelmonte|
And so it came about that on Easter morning, with his bride at his side, Messer Buondelmonte came riding over the bridge in a doublet of silk and mantle, with a wreath around his brow. No sooner had he arrived at the statue of Mars [at Ponte Vecchio], than Messer Schiatta degli Uberti rushed upon him and, striking him on the crown with his mace, brought him to earth. At once Messer Oddo Arrighi was on top of him and opened his veins with a knife. And having killed him, they fled.
The ambush had occurred at the houses of Amidei, who lived at the head of the bridge. Immediately there was a tremendous tumult. The body of the murdered man was placed on a bier, and the bride took her seat next to him, holding his head in her lap and weeping aloud. In this manner the procession moved through all Florence. And on this day, for the first time, new names were heard, those of the Guelf party and the Ghibelline party.
From a Cronaca attributed to a "pseudo Brunetto Latini": Ferdinand Schevill, Medieval and Renaissance Florence (1961), pp. 106-107
Mosca and Dante exchange words in Inferno 28.
See also this this account and here's another telling, by Thomas Adolphus Trollope.