Could any kind of learning be framed as learning a language? People learn (or actually acquire) languages naturally. As we grow up, we learn also multiple other skills which we then use in everyday life. 

A lot of these skills are often compared to a language, for example:


Mathematics
Reading
Playing musical instrument
Programming languages
Law
Playing chess (proven to rely on patterns)
Dancing
Painting or, more generally, producing works of art.


All of the above have been compared at one point to a language. They are used to communicate ideas, emotions and information. 

The language is used for communication. In the same way, one person knowing the law/programming language/accounting wouldn't actually possess any useful skill without the presence of other lawyers/computers/tax system. So one can argue that all these skills are relevant and can be evaluated only in the presence of other people who receive the message expressed using them.

In the same way, if one person invents their own language but nobody else understands it, we wouldn't classify it as a language.

So, could it be that most of the skills we learn could be described as a language? 
What would be arguments against it?
Is there any evidence I can look into with regards to similarities between learning different skills and learning languages?
It appears that the language and learning new skills would often (depending on the skill) be managed by different parts of the brain. It is, therefore, unlikely to be similar. 

A good description of how the learning process works from neuroscience's point of view can be found here: http://neuroscience.uth.tmc.edu/s4/chapter07.html.

This same course also describes how the language is managed in the brain in this chapter: http://neuroscience.uth.tmc.edu/s4/chapter08.html.

Based on the above, it doesn't seem to be the case that the mentioned skills are similar to language, at least not in terms of how the brain processes them.