All arts have a systematic component, however, it is not nearly as significant in the arts as it is in the sciences, philosophy and mathematics.
Today, Linguists almost unanimously believe that much of the structure of the language that we use is innate. The implication of this is that there is no need for a solidified tendency of thought in favor of seeking structure in order for one to enjoy language. A structure of logical thought is not innate and is therefore different from the structure of thought in language.
Poets and novelists for example know the structure of language very well, but they are artists rather than systematic thinkers. Most of them do not enjoy math, logic or the hard sciences and display no tendency of thought that is well suited for such activities.
1. Language is learned intuitively, many of the skills in learning it are innate, or inhere within our instincts. Math requires more systematic and non-intuitive thought. Some people are what you may call 'naturals' who seem to have an instinct to pick up on it, but nonetheless the tendency to learn math is not nearly as innate to human nature as the tendency to learn languages.
2. Language is indeed much less systematic than math or logic. In the language of symbolic logic, generally the same term almost never carries two different definitions. A dictionary often has 2 or 3 different definitions for the same word. Our communication both written and oral is filled with allegories, metaphors and even slang. All of these expressions are imprecise
Generally, language is much less precise than mathematical expressions. Mathematicians avoid using ordinary language as it is too imprecise for reasons I mentioned above. Altogether, the fact that there are so many confusions, disputes and gaps in communication regarding what people may have meant seems to show that expressions of language are ambiguous at best.