Gerontophobia is the fear of growing old, or a hatred or fear of the elderly. Many people have this phobia. The term comes from the Greek γέρων – gerōn, "old man" and φόβος – phobos, "fear".
Ageism
Discriminatory aspects of ageism have been strongly linked to gerontophobia. This unreasonable fear or hatred of the elderly is associated with the fact that someday all young people will grow old and that old age is associated with death. This unwillingness to accept death manifests in feelings of hostility and discriminatory acts towards the elderly.
References
Gerontophobia Wikipedia(Text) CC BY-SA