It’s a thorny problem but Philippe Nemo, a political philosopher, has an answer.
He says that five key episodes formed the West: (1) ancient Greece (reason, philosophy, education, democracy), (2) Rome (law, private property), (3) Christianity (linear idea of time, ethic of compassion), (4) the medieval papal revolution, and (5) the advent of modern liberalism in the 1700s and 1800s, particularly with the English, American, and French revolutions. The last, he thinks, were the most important: intellectual, political, and economic liberty now define what the West is.
So, the distinguishing feature of the West is liberalism, in the classic meaning of the term.
(Most French intellectuals who become influential in the English-speaking world are sworn foes of liberalism. Nemo is unusual. He openly admires the likes of Hayek and Popper.)
I am not entirely convinced.
Firstly, I would add another couple of key episodes to the list.
Second, I would not equate liberalism and the West. If the west is liberalism, would other civilizations that adopt liberalism thereby Westernize? Would the spread of liberalism mean there was no longer a distinctive West, just a universal civilization? If the West is defined by universal values, do its particularistic roots have no significance?
I think (classic) liberalism is one element of what the West is, but not the only feature. Also Nemo does not explain why the West (and particularly Northwest Europe, and especially England) pioneered liberalism.
Philippe Nemo, What Is the West? (Duquesne University Press, 2005).