Is there any practical reason to learn ancient Greek?
When we say “ancient Greek” we usually mean either BIblical Greek or pagan Greek. Pagan Greek has many uses for a person educated in the arts and sciences–a little Latin and Greek make the study of medicine much easier, for example, because you’ll know what thousands of the words mean without having to memorize them. Biblical Greek is something that helps you know when insincere or misinformed preachers are trying to build up their congregations by telling whoppers.
The practical reason to learn ancient Greek is to be able to read, or at least translate, ancient Greek. For most people, that may be of little or no “practical” use. However, it can be very useful is you want to study ancient Greek literature how it was written, help translate archeological finds, better understand Biblical Greek texts, or teach others ancient Greek. And of course, learning another language can just be a fun and interesting hobby in itself (as much as Sudoku, crossword puzzles, and other brain games) and you do get certain bragging rights.