What exactly, was the dispute between the two groups of shepherds?
Rashi: Lot's shepherds, who believed that the land belonged to Avraham and that Lot was Avraham's next of kin, allowed his animals to graze in other people's fields. 1
Ramban: When Avraham's shepherds would find suitable grazing-grounds, the shepherds of Lot would allow their sheep to graze on those lands. 2
In fact, the land was never promised to Avraham, but to his children, in which case, Lot's shepherds' claim was entirely unfounded (See Ramban).
Why does the Torah find it necessary to add that the Kena'ani and the Perizi were currently living there?
Rashi and Targum Yonasan: To point out Lot's shepherds' mistake, inasmuch as, since the land was currently in the possession of the Kena'ani and the Perizi, Avraham did not yet own it, in which case allowing Lot's sheep to graze there was pure theft. 1
Ramban: The land belonged to the Kena'anim, whose various tribes tended to move around (like nomads). Currently, it happened to be the Kena'ani and the Perizi, wealthy sheep-owners, who had set up tent there, the following year it might well be the Yevusi and the Emori.
Seforno: When the Kena'ani and the Perizi would see the "brothers" quarreling, it would make a bad impression on them, and, for fear that they might well turn against them, they would take action to prevent it.
Gur Aryeh: The end of the verse, "The Kena'ani and Perizi were then settling the land," shows that this was the point of disagreement. Otherwise, this phrase would be irrelevant.
QUESTIONS ON RASHI
Rashi writes: "They said, 'The Land was given to Avraham, and he has no heir; Lot is his heir.'" How does that justify their actions? Even a son who steals from his father [during his lifetime] is still a thief!
Gur Aryeh: [They reasoned that] HaSh-m would not grant an entire land to one individual; surely it was to Avraham along with his heirs. Therefore, they felt they had the right to assume possession of it already.
Rashi writes: "The land was given to Avraham... and Lot is his heir." If Lot and his men knew of HaSh-m's promise regarding the land, they surely knew as well of His promise to grant Avraham children! How did they presume to be the heirs?
Gur Aryeh: They reasoned that Avraham had already received the land upon his arrival, and the gift would not be rescinded; whereas the promise of children, they thought, would eventually be modified due to some sin on Avraham's part.
Rashi writes: "The verse informs us that... Avraham had not yet received [the Land]." Even notwithstanding this reason, we have just established that Lot would not be the heir!
Gur Aryeh: If that alone were the problem, Avraham had merely to grant permission to Lot to graze his flocks anywhere he pleased; there would have been no need for them to part ways. Rather, the issue was that Avraham himself had not yet been granted the land.