Dadophobia

Behavior by a woman or a man, apparently rooted in narcissistic anxiety, that mocks, shames, excludes or otherwise discriminates against Dads (i.e., men who show up for their children by taking paternity leave, engaging in nurturing behavior (especially in public), and juggling these demands with a paid job).

He took the paternity leave his employer offered even though he worried a bit about Dadophobia by his boss or even his wife.