I can't say that I know that much about animal communities because I don't come into much contact with animals but the aspect of communication which is beyond language is non verbal communication.

In daily interaction, this is central. Of course, we don't use it when we write but in actual conversation it can say so much. The smile, the frown and even the pauses can say more than words in many ways. Even on the telephone, we can hear emotions, such as the raised voice of anger or laughter with humour. So, I would say that understanding languages is about being able to go beyond words into the realm of the non verbal.

I can't say that I know that much about animal communities because I don't come into much contact with animals but the aspect of communication which is beyond language is non verbal communication.

In daily interaction, this is central. Of course, we don't use it when we write but in actual conversation it can say so much. The smile, the frown and even the pauses can say more than words in many ways. Even on the telephone, we can hear emotions, such as the raised voice of anger or laughter with humour. So, I would say that understanding languages is about being able to go beyond words into the realm of the non verbal. — Jack Cummins

I would go even further, and suggest that, in intellectualizing communication, we have actually introduced barriers to communication, wherein our sometimes faulty logic can lead us astray, sometimes we can end up in bad faith with ourselves. I think, at least within a species, animals cannot lie.

Absolutely, intellectualising can become a barrier and it can be a problem even in self talk. I don't think that cats lie awake in the middle of the night worrying about the meaning of life and they definitely don't get into philosophical arguments.

Of course, we don't really know what cats understand exactly. My mother used to talk to her cat, Plato, and she used to stand on the doorstep calling out his name at midnight, and he used to come running in. She used to say, 'He knows his name.'

But I wonder what cats make of loss or pain in the absence of language. For example, the cat is not able to have it communicated to her when her kittens are given away to others. Or, if a cat is ill, the vet is not able to give the cat an explanation, so the cat is left with unspoken truths in the absence of language.

I have a 3 month old pup. She responds to her name when called. The tone I use when calling her tells her if I want to play, I'm angry or I'm just trying to get her attention. Body language too plays a part. If I'm standing up and I ask her to get in her cage, she does so immediately. If I'm sitting down and I ask her to, she doesn't heed to my commands since she recognizes I won't be able to get to her quick enough to put her in. Those working closely with animals have figured out what different sounds and body language indicate. Especially when it comes to birds. Learning any 'language' takes time and interest. And even if you don't understand it, you know if somebody is being polite to you or is put off by you.

Thanks for all the valuable comments. On reading your posts I'm led to believe that,

1. We've understood or, at the very least, we've got a basic grasp of animal languages

2. Animal languages aren't about vocabulary in the sense we understand it - distinct words which by themselves carry semantic content - but are actually about, how shall I put it, pitch modulation. So, like on many occasions humans have participated in, it's not what you say but how you say it. So, for example, one can say "go home" with two different meanings - one could be a command, request for someone to go home and the other could be simply a question, "go home?", the difference between the two being simply their acoustic qualities.

So far so good. However, we're capable of this feat, in fact I believe our ability to express multiple meanings simply by modulating the acoustic qualities of our voice has peaked in humans and that takes us back to square one - human language is more complex and yet we;'re unable to understand animals, assuming of course that animal languages are simpler.

I think that what has happened is that we have allowed spoken language to supersede the more animalistic communications. This means that we look for meaning in the words and sentences of others rather than in the actions of others. So we ignore a whole world full of acts which actually have the most important meaning, thinking that anything important is spoken. Because of this we don't even seek the meaning of virtuous acts like loving, caring, and sharing, nor the opposing vicious acts.

humans, possessed of a more complex language, should be capable of understanding languages that are simpler, in fact too simple, like animal languages. Hence, The Too Simple Paradox Of Language. — TheMadFool

This sounds a bit like the "curse of knowledge/expertise":

The curse of knowledge is a cognitive bias that occurs when an individual, communicating with other individuals, unknowingly assumes that the others have the background to understand.[1] This bias is also called by some authors the curse of expertise,[2] although that term is also used to refer to various other phenomena.

For example, in a classroom setting, teachers have difficulty teaching novices because they cannot put themselves in the position of the student. A brilliant professor might no longer remember the difficulties that a young student encounters when learning a new subject. This curse of knowledge also explains the danger behind thinking about student learning based on what appears best to faculty members, as opposed to what has been verified with students.[3]
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Such research drew from Baruch Fischhoff's work in 1975 surrounding hindsight bias, a cognitive bias that knowing the outcome of a certain event makes it seem more predictable than may actually be true.[5] Research conducted by Fischhoff revealed that participants did not know that their outcome knowledge affected their responses, and, if they did know, they could still not ignore or defeat the effects of the bias. Study participants could not accurately reconstruct their previous, less knowledgeable states of mind, which directly relates to the curse of knowledge. This poor reconstruction was theorized by Fischhoff to be because the participant was "anchored in the hindsightful state of mind created by receipt of knowledge".[6] This receipt of knowledge returns to the idea of the curse proposed by Camerer, Loewenstein, and Weber: a knowledgeable person cannot accurately reconstruct what a person, be it themselves or someone else, without the knowledge would think, or how they would act. In his paper, Fischhoff questions the failure to empathize with ourselves in less knowledgeable states, and notes that how well people manage to reconstruct perceptions of lesser informed others is a crucial question for historians and "all human understanding".[6]
https://en.wikipedia.org/wiki/Curse_of_knowledge