What is the ruling on one person saying to another “Eat air (i.e., shut up)” as a put-down?

Making fun of people and insulting them is something that the Muslim should be above doing.  It is one of the things that Allaah has forbidden the believers to do because it generates resentment and hatred among the Muslims, and because it stems from arrogance and feelings of superiority on the part of the one who is mocking and insulting the other. There are strong warnings issued to those who are arrogant and look down on people. 

It was narrated from Ibn Mas’ood that the Prophet (peace and blessings of Allaah be upon him) said: “No one in whose heart is a mustard seed’s worth of pride will enter Paradise.” A man said, “What if a man likes his clothes and his shoes to look good?” He said, ‘Allaah is Beautiful and loves beauty. Pride means disdaining the truth and looking at people with contempt.”

(Narrated by Muslim, 9) 

One of the qualities of the Muslim is that the Muslims are safe from his words and his actions. 

It was narrated from ‘Abd-Allaah ibn ‘Amr ibn al-‘Aas that a man asked the Messenger of Allaah (peace and blessings of Allaah be upon him) which of the Muslims was best? He said, “The one from whose words and actions the Muslims are safe.” (Narrated by al-Bukhaari, 10; Muslim, 40). 

The phrase which the questioner asked about does not involve anything that is haraam in sharee’ah as far as the words themselves are concerned, but we wish that they were not uttered by a Muslim because of what they imply and because of the resentment and hatred that they may lead to.