In his inaugural lecture (.pdf, in Dutch), University of Leiden microvariationist Marc Van Oostendorp talks about how linguistics, or many other forms of fundamental research, is not socially relevant. He lists a number of basic answers.
1. The outcomes of fundamental research are difficult to predict (cf. mathematics => computer science => Facebook => B4-4);
2. Acquiring knowledge is a fundamentally human trait and science is a highly (if not the highest) developed form of cultural expression;
3. Researching seemingly irrelevant subjects bears directly on a demand that many hold to be the first step in making sense of this life of ours: know thyself.