It might have been an argument over material things, but this is not how Rashi explains the verse.
He says it was a conflict over ethics.
Abraham’s servants had been trained in their master’s ways and automatically lived by Abraham’s moral principles. Lot had more elastic principles and had not trained his servants to be so particularly scrupulous.
Hence, says Rashi, Lot’s shepherds led their flocks into pastures that belonged to other people; not for them the strict moral duty not to encroach on another’s territory (Deut. 19:14).
Abraham’s shepherds rebuked Lot’s men, who answered that God had promised the whole land to Abraham in any case, and since Abraham had no children at this point, Lot was his heir and entitled to go anywhere.
Two attitudes, two sets of ethics.
Yes, there was a Divine promise, but the promise did not justify anyone acting without respect for the rights and feelings of others.