Long ago I thought of the human voice as an instrument, just in a different family than brasses and woodwinds and strings and electronics, but I now think of flutes and violins and synthesizers as surrogate voices. There can be no doubt that music that used pitches originated with the voice, probably eons before the first external devices.
So what makes the voice “not an instrument”? First of all, vocal sound is made with the living tissue of a human being. There is no manufactured implement involved. Also, for the last few thousand years, vocal music has involved words. This element alone puts it in a completely different category from wordless music-making. Yes, there are a few pieces like Ravel’s Vocalise-étude en forme de habanera, Rachmaninoff’s Vocalise, and Gliere’s Concerto for Coloratura Soprano that don’t use words. In these cases the voice could be said to be like an instrument. But still the sound is made with a living human body directly, and not with a manufactured object.
I think there are deeper reasons why the voice is not an instrument in addition to the fact that you cannot separate the instrument from the person physically. The same voice with which you speak and cry out in pain or pleasure is the same voice with which you sing. It is primal. It is a deep and inseparable part of being human, not just a body. You cannot say that about a clarinet.
Sometimes singers try to get some psychological separation from their voices. They say “my voice” or sometimes even “the voice” when referring to their singing voice. A singer needs this distance occasionally to keep from being obsessed with its use and care all the time. There may come a time when a singer is unable or unwilling to sing, and having the singing voice be a thing apart from the speaking voice can make more mental and emotional space for the rest of life. In the case of the high-level performer, there is also a big difference between singing a lullaby for a grandchild and performing on a stage. These two scenarios may not use the same “voice” in psychological terms.
I get a strange, visceral, negative reaction to a singer talking about “my instrument” when they refer to their singing voice. It seems like enough of an objectification to say “my voice” or “my singing voice” or “the voice”, but to say “my instrument” turns it into a machine to own and operate, and messes with my sense of the primal, true, human element that needs to be intact for one’s vocal expression. Even in this strange era of alienation and technology, calling one’s personal bodily means of making music an “instrument” feels wrong.
Correspondingly, I don’t feel that “singing” is “playing an instrument” although both are “musical performances”. Singing involves a synthesis of expression that playing a tuba does not. The instrumentalist does not use elements of speech, hands, and face as part of the expression.
I have studied several instruments with the best teachers I could find. Every one of them encouraged their students to “sing” on their instruments. They all encouraged emulation of excellent singers. I have never had a voice teacher or coach ask me to play my voice more like a violin or saxophone, except for a novel, usually comedic, effect. And even then, I was still expressing words, which is a whole different world from playing a melody.