The phrase "how-do-you-do" is an informal greeting, but when it comes to antonyms, there aren't many options. One antonym could be aloofness, meaning being distant and unfriendly. Another antonym could be hostility, meaning showing aggressive behavior or animosity towards someone. Additionally, indifference or apathy could be considered an antonym, as it suggests a lack of interest or concern towards someone else. However, it's important to note that these antonyms are not directly interchangeable with "how-do-you-do", as they are not standard greetings.