I’ll need to find the exact chapter later but in Rabbi Avigdor Miller’s work, “Rejoice O’ Youth”, this question or some variation of it is asked. The sage in the work responds that it wasn’t really Avraham that was chosen, rather Shem. Although Shem was a Tzadik and ultimately learned, he didn’t promulgate the name of Hashem; rather, he kept to himself learning (and opened a yeshivah). The following descendants were then tasked with the promotion of Hashem‘s name but for some attribute or lack thereof they did not. Idolatry was eventually popularized and this further cascaded the degradation of the descendants. We are then led up to Terach and then Avraham. As I aforementioned, the descendants of Shem, each and every one of them could have been the one to be the progenitor of Bnei Yisroel. Avraham’s paradigm shifts and at some point in his life he concludes the prevailing doctrine of Monotheism. That which Avraham fulfilled was in actuality supposed to have been fulfilled by Shem. In addition, R Miller expounds the fact that Avraham was no ordinary individual but one with capacities of great breadth. Any field of endeavor wasn’t elusive for him. He apparently was learned in many different wisdoms and if he didn’t live up to his challenges he could have claimed rulership over some part of his land. His ancestors possessed similar dexterities too.
I didn’t necessarily answer your question, as you could ask further “then why was Shem picked”, but that leaves out that the arbitrary selection of a random descendent from a particular lineage, as opposed to a selection of three brothers, and this selection was clearly not arbitrary, given their actions upon departure of the Tevah.