What is the most likely reason that American law has many Latin terms?

American law has its roots in British law. In turn, British law can trace its history back to the time of the Roman occupation in some cases. However, many of the British laws were written in Latin, being the language of scholars and academics in the country for many centuries after the Romans packed up and left.

Although much of the Latin is being removed from British law, some still remain and are likely to remain as they are effectively adopted into the English Language. The same is the case in the US where Latin terms are perhaps sounding strange these days but remain perfectly understood.