The word ephebiphobia, meaning fear of young people, has appeared in several newspaper articles recently (this Guardian feature, for instance). The word does not appear (yet) in the Oxford English Dictionary. It is believed to have been coined in 1994 by Kirk A Astroph in an article in the professional education journal Phi Delta Kappan (abstract here).
Ephebos is Greek for 'youth or adolescent', and phobia is Greek for 'fear'. The OED has a handful of related entries, including the nouns:
ephebe, ephebus - in ancient Greece, a young citizen aged between 18 and 20
ephebeum - a court in the palaestra for young men to exercise themselves
ephebiatrics - the branch of medicine dealing with the study of adolescence and the diseases of young adults
ephebophilia - sexual attraction in adults to adolescents especially homosexual attraction to adolescent males
The words ephebriatics and ephebophilia were coined in the mid-20th century.
Hebe- is another prefix related to puberty (perhaps a bit younger than epheb-); the citations for hebephrenia tell us that it is the insanity of puberty, characterised by silliness, incongruity and mannerisms. In theory, people who fear or dislike young people could be accused of ageism (defined in the OED as "prejudice or discrimination against people on the grounds of age"), but ageism is usually directed against the older members of society (as the OED goes on to say).