Linguistics is the scientific study of language as a system rather than the study of specific languages. Previous teaching experience is not usually relevant for an MA linguistics and mathematical and scientific skills are as important as linguistic skill, in other words, knowledge of other languages. A Linguistics MA will cover things related to English language teaching such as phonology, second language acquisition and sociolinguistics but will not usually cover the teaching of language directly.
MA Linguistics is one of a number of Masters, or MAs as they are commonly known, which have a higher concentration on theory and focus less on classroom practise than MA Tesols and other teaching related MAs. English language teaching is just one of the areas covered in these degrees and an Applied Linguistics MA or MA Linguistics does often not require teaching experience but will require a good first degree.