Why does Indian Hindustani or Carnatic music not use chords in compositions? I haven't seen any composition that mentioned about chords. Were Indians not aware of chords?
There are some chords, but they're used in a bit of a different way than the Western classical tradition. It's a stylistic feature of these two genres owing to their origins in the late Medieval and early Renaissance eras.
They both highlight the raga (basically a melodic pattern) and tala (a rhythmic pattern), just like the respective color and talea of the isorhythmic tradition in Central Europe around the same time.
But whereas the isorhythmic tradition often emphasized the motet (and thus polyphony), the Hindustani and Carnatic traditions tend to emphasize a single voice (or vocal line) in a homophonic texture. Often this doesn't result in chords, but sometimes it does.
It's not that they didn't always think of chords, it's just that this is a stylistic trait. It's a bit like asking why Dickens never wrote an illustrated children's book. He could've, he just didn't. (At least I don't think he did.)
All traditions of a culture are inter-related. Indian philosophies have focused on the individual not collective. Music is a path for an individual to seek bliss or its variants. Every element of music then immediately takes on either an individual or supportive role. This gives every swara (simplistically a note) a status and character. This explains why creating a sound by combining multiple frequencies is missing. In its place, Indian music works with microtones between swaras.