These characters combine literally to mean “to get halfway down the road and then abandon it.” This imagery is the core of the idiom's meaning: abandoning an endeavor after it's already underway.
The idiom 半途而废 (bàntú'érfèi) is deeply woven into the Chinese cultural emphasis on 毅力 (yìlì) - perseverance and 有始有终 (yǒushǐ yǒuzhōng) - finishing what one starts. These are not just positive traits but are often seen as moral virtues. This idiom is famously associated with the story of Lè Yángzǐ (乐羊子) from the Book of the Later Han (后汉书). Lè Yángzǐ was a scholar who left home to study. After only one year, he returned, homesick. His wife, who had been weaving silk, took a knife and cut the fabric in half on her loom. She told him, “My cutting this silk is like you abandoning your studies. If you give up halfway, all your previous effort is wasted.” Ashamed, Lè Yángzǐ returned to his studies and did not come back for seven years, eventually becoming a great official. This story highlights the cultural weight of the idiom. 半途而废 is not a neutral, strategic decision like it can be in the West. While an American entrepreneur might be praised for “failing fast” to cut losses on a bad idea, the traditional Chinese perspective sees 半途而废 as a failure of character. It represents a waste of resources, time, and—most importantly—initial resolve.
半途而废 is a formal idiom, but it's widely understood and used in everyday conversation. Its connotation is almost always negative and critical.