The phrase "neat as a button" implies that something is orderly, tidy, and well-organized. Some antonyms for this phrase include messy, disorderly, unkempt, disorganized, and sloppy. These words describe a lack of cleanliness, tidiness, and orderliness, and might be used to describe a cluttered desk or a room that has not been cleaned in a while. Messy can also refer to someone who is careless or lacking in attention to detail. In any case, these antonyms denote a lack of precision, carefulness, and cleanliness, which the phrase "neat as a button" suggests.