In the book, Murmurs of Earth, Linda Salzman Sagan explained how and why she and her husband selected the contents of the Voyager Golden Records:

We were principally concerned with the needs of people on Earth during this section of the recording. We recorded messages from populations all over the globe, each representative speaking in the language of his or her people, instead of sending greetings in one or two languages accompanied by keys for their decipherment. We were aware that the latter alternative might have given the extraterrestrials a better chance of understanding the words precisely, though it would have raised the thorny question of which two languages to send. We felt it was fitting that Voyager greet the universe as a representative of one community, albeit a complex one consisting of many parts. At least the fact that many different languages are represented should be clear from the very existence of a set of short statements separated by pauses and from internal evidence - such as the initial greeting "Namaste," which begins many of the greetings from the Indian subcontinent. The greetings are an aural Gestalt, in which each culture is a contributing voice in the choir. After all, by sending a spaceship out of our solar system, we are making an effort to de-provincialize, to rise above our nationalistic interests and join a commonwealth of space-faring societies, if one exists.

We made a special effort to record those languages spoken by the vast majority of the world's inhabitants. Since all research and technical work on the record had to be accomplished within a period of weeks, we began with a list of the world's most widely spoken languages, which was provided by Dr. Steven Soter of Cornell. Carl suggested that we record the twenty five most widely spoken languages. If we were able to accomplish that, and still had time, we would then try to include as many other languages as we could.

The organization of recording sessions and the arduous legwork involved in finding, contacting and convincing individual speakers was handled by Shirley Arden, Carl's executive assistant, Wendy Gradison, then Carl's editorial assistant, Dr. Steven Soter, and me. The master table, reproduce on pages 134 through 143, which shows each of the languages, the speaker's name, their comments in the original language, an English translation, and the real and fractional number of human beings who speak that language, was largely Shirley's idea. We contacted various members of the Cornell language departments, who cooperated with us on very short notice and provided numerous speakers, even though school was ending and many people were leaving for summer vacations. Other speakers were more difficult to find. sometimes it meant sitting for hours, telephoning friends of friends who might know someone who could speak, let's say, the Chinese Wu dialect. After finding such a person, we had to determine whether he or she would be available during the hours when the recording sessions had been scheduled. Even while the recording sessions were going on, were were still trying to find and recruit speakers of languages not yet represented. Often people waiting to record would suggest names of individuals fluent in the very languages we were looking for. Immediately we called those people, explained the project and our plight, and asked them to come at once. Many people did just that.

Bishun Khare, a senior physicist in the Laboratory for Planetary Studies, was responsible almost singlehandedly [sic] for the participation of the Indian speakers. He personally called friends and members of the Cornell Indian community, explaining the undertaking to them and asked for and received their cooperation.

There were only a few disappointments, where someone had agreed to come to a recording session, could not and forgot to let us know in time for us to make other arrangements. It wasn't always possible to find replacements at the last minute, so there are some regrettable omissions - Swahili is one."

That's about all the info I could find. It seems like the choice of languages was unfortunately partially determined by the availability of fluent speakers in the vicinity of Cornell University during a few weeks in the summer of 1976, when all these recordings were made.