The phrase "gave a leg up" implies aiding someone or something towards success, growth, or improvement. Antonyms for this phrase could include hindering, obstructing, impeding, or undermining. Instead of giving someone a leg up, people who hinder may cause obstruction or delay. Those who obstruct intentionally prevent progress or hinder advancement. Impeding suggests slowing down or stopping someone's advancement, while undermining is to weaken, diminish, or sabotage progress. Therefore, antonyms for "gave a leg up" are verbs that hinder or obstruct progress, rather than support or facilitate it.