The film plays with the concept of language influencing thoughts. At one point it drops a hint, when dr Banks dreams up a conversation with Ian where he mentions the Sapir-Whorf hypothesis, which was a rather strong version of the idea (where language determines thought).
The language of the heptapods is described in the film, both in conversation and visually by the use of circular patterns as not having the concept of a beginning and the end of an utterance. All sentences are formed already whole, so in the accordance with the aforementioned hypothesis, one can imagine their thoughts being similarly already-formed, with no perception of what's before and what's after.
The conceit here (the 'fiction' bit in the S-F that we need to suspend our disbelief for) is that this extends to the whole of their existence, that they see all of their life experiences as already existing, rather than being a series of temporally-ordered events one has to either wait for or remember. When Banks begins to learn their language, she begins to 'remember' her whole life (i.e. see the future) - but there's more. As in this new way of seeing the world there is no beginning and no end, and all of experiences exist at once, it means that she has always known what she will ever know. That her flashbacks (premonitions? flash-forwards?) did not begin only after she learned the language.
That she doesn't always understand what's going on, or doesn't remember everything, can be blamed on it being an alien language that she struggles (have struggled, will struggle) to grasp in its entirety. It all fits rather nicely, I thought.As for why didn't the aliens learn human instead - it's a film about communication. About meeting half-way and understanding each other. But also about the concept of 'uplifting' by a more advanced race. One can argue that the most advanced 'technology' the aliens wanted to transfer was their language with everything it makes possible.
