Antonyms for the phrase "gave a boost to" might include "held back," "discouraged," or "impeded." For example, if a person or event "held back" a project, this would mean that they prevented it from progressing, rather than giving it a boost to move forward. Conversely, to "discourage" something means to actively dissuade it from continuing, whereas boosting would mean to inspire and motivate it. Lastly, to "impede" something would be to prevent it from moving forward, rather than giving it the necessary momentum to succeed. These antonyms provide a contrast to the positive connotations of "gave a boost to," emphasizing a lack of progress or even failure.