Abu Qatadah (May Allah be pleased with him) said: The Prophet (PBUH) said, "Do not touch your private parts with your right hand while urinating, nor for washing or cleaning (your private parts); and do not breathe into the drinking vessel from which you drink."[Al-Bukhari and Muslim].
Muslims are required to take food and do other such things with their right hand. They have been ordained to do all the other essential but not much liked acts with their left hand. This demarcation has been done to highlight the distinctive position of the right hand. It is regrettable indeed that some Muslims nowadays use the left hand for eating. It is a sign that their righteous nature is spoiled and that they have totally ignored the Divine injunctions. May Allah help us observe the Divine orders.