Why read fairytales, or write them, or think about them? It is more than a matter of taste, as of liking chocolate, or disliking it. There are several reasons why I think it is worthwhile to read fairytales. Usually I would begin this discussion with a rough definition of what a fairy tale is, but I think I can safely assume that everyone has a general idea of what a fairy tale is, and go from there (for instance, Ever After is obviously the story of Cinderella, although it contains nothing of the fantastic, and Redwall is not a fairy tale, though it contains talking animals). If you want a good definition of fairy tales, I would suggest Tolkien's essay On Fairy Stories.
Fairy tales are one of the few modern mythologies. I am not suggesting that anyone believes in the literal existence of fairy godmothers, or the real historical existence of Cinderella. However, fairy tales are so prevalent that they have crept into our common language. They may be ignored, or they may be loved or hated, but their influence is obvious. Many people talk about "happily ever after" and "once upon a time", about a "knight on a white horse" and a "princess in a tower." These are all fairy tale tropes. Movies like Shrek or Enchanted are dependent on a widespread understanding of fairy tales in order to make any kind of sense. And, of course, there are the many retellings of Cinderella, Snow White, and Briar Rose, to name just a few.
Fairy tales are mythic because there is no one definitive version. There are many versions of Cinderella, from the Disney movie to Ever After to Ella Enchanted. But no one story or version contains all that is to be said, or can be said of Cinderella. The story exists in various incarnations, but it also exists independent of the various forms in which we may encounter this. Compare this to, for instance, Pride and Prejudice. The book is compelling, one of the great works of literature, yet it is dependent on the language and atmosphere of the English Regency. However, fairy tales have a certain independency of setting and form. Cinderella may be found in Los Angeles, in generally historic past (think of Ever After), or in a fantastic past (think of the Disney version), or in an entirely different world (think of Ella Enchanted). Fairy tales may be told as simply as a few pages, or may be an entire novel.
Fairy tales are lasting and durable. Now, by this definition, not everything that is called a fairy tale or is found within the pages of a fairy tale collection is, in fact, a fairy tale. There are many stories that have disappeared into obscurity, often with good cause. However, the great stories are lasting, and Beauty and the Beast is still as powerful today, in all its incarnations and manifestations, and the day it was first penned in France.
Fairy tales deal with important and lasting ideas, but cannot be distilled into mere summations. One of the ideas of Briar Rose, for instance, is that love can conquer time and even death itself. But even stating all the ideas contained within a fairy tale, if such a thing is possible, does not explain away the fairy tale. The story contains more than can be stated propositionally (as opposed to poorly written allegories, which contain only that which can be stated propositionally). The images found within fairy tales, of the great briars around the castle, of the single glass slipper or the golden apple, are as important as the ideas found within fairy tales, such as the reward of virtue with happiness, of the redemptive nature of love, or of justice tempered by mercy.
You may like fairy tales, or dislike them, you may reject them or embrace them, but fairy tales are worth thinking about. To conclude, I will say that fairy tales are mythic, and you ignore them at your own peril.