It is the fondness for palindromes. The etymology is humorous since it is a word that is read the same from left to right and vice versa, from the suffix -filia (as a hobby). [Note: there is a published definition of aliphobia with a Greek origin, but it could also be (wrongly) inspired by 'ailifilia'.]
* Only one "like" per meaning and day, the more "likes" the meaning will appear higher in the list