The phrase "giving a boost to" means to help or support something, so antonyms for this could include words like hinder, harm, damage, weaken, undercut, or obstruct. These words imply a negative impact rather than a positive one, suggesting that the actions or events in question are not helping to achieve a desirable outcome. Antonyms for "giving a boost to" could be used, for example, when discussing factors that are holding back progress, or when describing obstacles that must be overcome in order to achieve success. By using antonyms like these, speakers or writers can add nuance and complexity to their language, highlighting both positive and negative influences on a situation.