The antonyms for the phrase "carrying through" could include terms such as abandoning, giving up, quitting, or faltering. These words all suggest a lack of commitment to a goal or task, and a willingness to let it go unfinished or incomplete. For example, if someone were tasked with completing a project, but abandoned it halfway through, they would not be carrying it through to completion. Similarly, if someone were to give up on their dreams or aspirations, they would not be carrying them through to fruition. In both cases, the lack of follow-through results in an outcome that is less than optimal.