Attic Greek ( https://en.wikipedia.org/wiki/Attic_Greek
) is the language that was spoken in Attica (Athens area) in the 5th century BC, during the peak of the ancient Greek civilization. Greeks study it in public schools, because this is the language of most important and famous writings of ancient Greek philosophers and poets.
Koine Greek was a later (3rd century BC) evolutionary stage of the Greek language. It was more simple than Attic Greek, because it was spoken by many nations, after Alexander’s conquests and spread of the Greek civilization.
Koine Greek is considered simpler and easier to learn than Attic Greek. For this reason it may be the preferred version for people to learn outside Greece. However very few people study it in Greece.