How did God choose Abram to start the nation of Israel?

God chose Abram by sovereignly singling him out from an idolatrous, pagan family that had no knowledge of the one true God. He appeared to Abram, spoke directly to him, and commanded him to leave his country, kindred, and father's house for a land God would show him, beginning Israel in Genesis 12.

Les explains that the nation of Israel did not come about by accident; it began back in Genesis 12. The Lord had said in chapter 11 to Abram, "Get thee out of thy country, from thy kindred, and from thy father's house." Abram's family were idolaters, idol worshipers, and pagans who had no knowledge of the one true God. Out of that whole then-known world saturated with pagan worship, God put the finger on one man, appeared to him, and spoke to him, giving him instructions to leave his idolatrous family, make the break from paganism, and go to a land God would show him. Les also notes that Abram was not totally obedient, and he places the blame on his father, who said they would go with him. God then stopped him halfway between Ur and Canaan until his father died.

Genesis 12:1

Now the LORD had said unto Abram, Get thee out of thy country, and from thy kindred, and from thy father’s house, unto a land that I will shew thee:

Why did God tell Abram to leave his family and country?

God told Abram to leave his country, kindred, and father's house because Abram's family were idolaters, idol worshipers, and pagans with no knowledge of the one true God. God was separating him from paganism to go to a land He would show him.