In short: chance, followed by isolation.

Before the late 19th century, there was no international standard for writing dates. In both Great Britain and the American colonies, people used two formats interchangeably.

• You could write Month-Day-Year (e.g., "October 31st, 1776"), which matched the spoken phrase "October 31st."
• Or, you could write Day-Month-Year (e.g., "the 31st of October, 1776"), matching the spoken phrase "the 31st of October."

Because the British Empire colonized America during a period when Month-Day-Year happened to be incredibly common, early Americans adopted it as their standard format.

However, during the late 19th and early 20th centuries, global trade, international shipping, and telegraph networks expanded. Great Britain sought to standardize its systems to align with continental Europe, which favored the Day/Month/Year format because it is strictly logical and hierarchical.

Ultimately, while Britain altered its habits to match Europe, the United States remained geographically isolated across the Atlantic and saw no pressing economic reason to change. The exact same thing happened with the adoption of the Imperial system (feet versus meters).