Why was being a descendant of Abraham such a big deal to Jews?
Being a descendant of Abraham was the crowning bragging right of a Jew, the highest source of pride and identity. It was their boast as sons of Abraham, and Paul matched that claim by saying he also was the seed of Abraham, leaving opponents nothing to hold over him.
In 2 Corinthians 11:22, Paul is answering opponents, likely Peter and the eleven, who boasted of being Hebrews, Israelites, and the seed of Abraham. The seed of Abraham was the crowning bragging right of a Jew—the fact that he was a son of Abraham. Paul responds to each claim with 'So am I,' showing they had nothing on him. He then lists his labors, stripes, prisons, and deaths to demonstrate his own apostolic credentials.
Are they Hebrews? so am I. Are they Israelites? so am I. Are they the seed of Abraham? so am I.