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.