It is absolutely impossible. Actually a suicidal idea.
The stronger a light shines the darker are the shadows around it.
Also if we dont eat non-vegetarian, in that case, animals will still eat plants but we won't eat them then we need to grow more plants to fulfil ours and animal hunger which seems to be difficult.
Further, the rates of cereals will increase due to an increase in the demand. Also, many people will get unemployed as people are employed in food processing units and farming animals like sheep, hens and other animals.
" The two most important days in your life are the day when you are born and the day you find out why? "
– Mark Twain
So even if all the people want to convert themselves from meat eating to vegetable eating, it will not be practically possible to do so.
Thoughts exchanged is knowledge gained.
For being non-vegetarian, the justification is given that we got enough livestock & if not killed than there will be unprecedented increase in their population but in between we forget that there is an ecosystem which getting adjusted automatically but due to much interferences of the humans this not being done.
Unfortunately, many of our good imaginations do not see the light of the day due to practical limitations and this is also one such case. As other members have rightly pointed out there is already a shortage of vegetarian food and avoiding the big source of non vegetarian food will create a situation of chaos only.
Knowledge is power.
So, please don't force vegetarianism on all of us.
"If you are killed in action, you go to Heaven. If you win, you rule this Earth (as beautiful as Heaven). That is why, O son of Kunti, take a firm resolve and fight!"-- Shrimad Bhagwad Gita
The availability of vegetables will become less. We have to face a severe scarcity of vegetables and the cost of the vegetable will go very high. The availability will be very less and may have to be supplied through ration shops and in the black markets rates will be adsorbent. The cultivation of vegetables is to be increased manifold and a lot of research is to be carried out to get the desired output.
Similar to this the pure vegetarian mentality should come in self and not by any individual compulsion or prohibition.
Already we have cut down so many trees and the pollution is rising at an alarming level, so there is not sufficient greenery for us. The animal rights activists are carrying out different movements to stop torture of animals. I am afraid, if everybody turn to eat vegetables then we may find plant rights activists too protesting against the indiscriminate consumption of vegetables.
"Life is easier when you enjoy what you do"