Another way of looking at the problem:
Think of communication as a game. Create a whiteboard in your mind. Draw two cartoon guys facing one another. The left guy wants to communicate a concept to the right guy. Draw in the left guy's cartoon head some representation of a set of cognitive states. The game of communication is for the left guy to somehow create those same states inside the head of the right guy.
Between two humans this is trivial as long as they are playing a common second game (they share a common natural language). But all human natural languages are really just the same language. There actually is only one language. An interesting fact about humans.. our language seems to be evolved and is unique to the condition of our species. Different natural languages are differing dialects of the a tree of dialects of the same language. We can even trace them back in time to only a few handful of languages. Some thing we can infer some of the words in the original ancestral language of our species, but I have my doubts.
An alien does not share any of that. They don't share a common evolutionary trajectory as us. They don't share our bodies. Their environment is likely very different, with different problems. Their brains, if they even have a single brain like we do, are different. They don't even share the same cognitive states as us.
How in Space are you supposed to create in the mind of an alien the semantic states you are holding in your conscious mind? What if the alien is not even a conscious creature to begin with? They could be running on biological programs that solve problems in a completely different strategy from us.
In my opinion, there are two games: communication and language. The game of communication is to elicit a set of states in another person's minds (transmission of an idea, feeling, whatever). The game of language is working out grammatical rules, semantics, lexical differences, etc. to accurately (or possibly deliberately not) convey information. Sometimes the game of communication is manipulation, where the sender is trying to elicit a behavioral response, not necessarily create an accurate cognitive state. In any case, I don't think the problem of communicating with actual aliens is obvious or trivial. At all.