There are a couple of reasons to cut out eggs. The number one reason is for the chickens. Chickens are the least protected livestock. The number of chickens slaughtered each year is in the billions. Environmentally speaking, chickens aren't as bad as cows. But they are ... I heard a good term the other day.... living weapons of environmental mass destruction. Their excrement is incredibly toxic and chicken farms don't treat their sewage. It just gets washed downstream. Yes, a lot of chicken manure goes into fertilizers. but there is just so much. and much just flows into places like the chesapeake bay.
Oh wait, you were talking about eggs. well, that's ok. egg production is even worse than chicken production. Layers have it even worse than broilers. Presently there are over 300 million laying chickens in the USA. And although the damage to the environment isn't quite as bad as it if for chicken meat, its pretty significant.
Now eggs are a good cheap source of protein. but there are plenty of good cheap sources of plant protein. a gram of protein you get from an egg is about 2.5¢. Which makes it (probably) the lowest price per gram of animal protein. I was going to list plants that were cheaper sources of protein. but there were too many. Ok, how bout I list the plants with higher costs for protein... um... can't find any. check the link below.
http://plenteousveg.com/cost-vegan-protein-vs-animal-protein/
Ok what about health risks. You hear over and over how eggs got a bad rap. that saturated fat and cholesterol aren't bad for you. OHMY. The egg board has done an amazing job of providing factoids to back that up, too.
but its just not true. there are no minimum amounts for cholesterol in our diets. If we don't eat any (cause we are vegan) our bodies will make some. There are very few non-vegan Americans who need more cholesterol in their diets. Two eggs puts you over the RDA of cholesterol.
The AHA recommends about 12 grams of saturated fats in our diets. Two eggs have three. but too much cholesterol. and are you currently below the RDA for sat fats? If you are, just use a tablespoon of cooking oil in your stir fry. Even vegans have a hard time minimizing their saturated fats to the point you need to eat some on purpose.
as far as B12 goes, its probably already in your plant milk. 2 - 3 glasses a day should put you over the mRDA. plus the latest medical research says you should get your B-12 in small does spread out throughout out the day. Lots of breakfast cereals have B12 added too. But I always recommend a daily multivitamin, it has b12 and maybe some other vitamins you need every day.
So basically there is nothing essential or necessary in an egg and there are good ethical, environmental and health reasons not to eat them. so go fully vegan.