> Is it impossible that humans could build a system to know what a whale wants, based on its vocalization, that does better than the typical whale?

The answer resides in the question. For a human to know what a whale wants is to have an understanding of what it is to be a whale, not deriving a Rosetta Stone[0] such that bidirectional vocalizations could be exchanged.

So is it possible to communicate with a whale? Sure.

But the infeasiblity of cross-species understanding is far more difficult than even what you identified above:

  ... despite having similar biology and wants, humans 
  misunderstand others' intents and miss cues a lot.

Now add to all of this the fact that computer algorithms are just that, and not even having the shared commonality of being mammals, and the possibility of a machine understanding what a human wants is fantastical at best.

0 - https://en.wikipedia.org/wiki/Rosetta_Stone

I think this is a silly take. Not all species had evolutionary pressure for cross-organism understanding. A different species that has selective pressure for social understanding and greater mental understanding is probably going to understand what an insect wants better than say, another insect.

That is, how well you can understand someone else doesn't depend just on common ground, but perhaps even more on how mature of machinery for understanding that you have.

> That is, how well you can understand someone else doesn't depend just on common ground, but perhaps even more on how mature of machinery for understanding that you have.

I disagree, and believe I can explain why.

If I wrote:

  I can think of a few HN posts I have written which did not
  properly express my intent when I wrote them.

Is this a statement that you can relate with?

Even if not, does it communicate an experience you could envision based on your being a participant in this forum, having written posts yourself, and knowing I am a person just as you are doing the same?

What if I texted the sentence to someone who has never heard of HN?

Now what would happen if I wrote that same sentence on a piece of paper and handed it to a random person in a train station where no one spoke English?