No. Opinions and personal desires aside, fairies belong with mermaids, vampires, unicorns etc. They are purely mythical and fantasy creatures and creations of the imagination.
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It is not physically possible to become a Fairy, and it is also very difficult to discover one, too. If you hear bells, or smell cinnamon, or perhaps both, you might want to start looking around,...
The only instance of 'becoming a fairy' that I know of wasn't exactly a fairy but a water baby. The process is outlined twice in the novel 'Water Babies'.