Little Brother Syndrome

When a person/organization/whatever noun (#1) feels a rivalry with another person/org/noun (#2), and does everything they can to feel like they are beating the other group, meanwhile person (#2) does not recognize the rivalry at all or does not consider person (#!) a threat.
Named this way because little brothers have a knack for being annoying puntable things

Greg totally has Little Brother Syndrome, when he heard Alysa read 25 pages he read 30 just to be better than her. Little does he know "Learn ABC's with Caillou" is not on par with "War and Peace."