You can get both essential ω-3 and ω-6 short chain polyunsaturated fatty acids from flaxseed, without the baggage of eggs (high cholesterol) and fish oil (high levels of persistent organic pollutants).
Additionally, eggs are very high in arachidonic acid, which is the thing your body actually needs (linoleic acid is only essential as a precursor to arachidonic acid production), and the eggs I buy also contain very high levels of vitamin D, vitamin E and iodine.
As for the fish oil, I buy a high quality supplement that claims to be extremely high purity (though of course this being supplements, that could mean anything). The rational for fish oil over flax is that it contains EPA/DHA, which are the fatty acids that are actually responsible for most of the beneficial effects; your body is pretty poor at metabolizing alpha-linolenic acid to EPA/DHA.
Its greatest advantage is that the seed does not need to be milled (exposing the oils inside to light and oxygen) to be digested. Second, it has more of that mucilaginous fiber coating than flax, making beverages such as chia fresca possible. Third, I just like the flavor better. The disadvantage is cost per kg. Chia still costs more than flax.
But one need not pick just one or the other; they're both excellent foods.
Non-vegans can go lower on the food chain than fish oil by eating krill oil. Krill are only one step up from algae. In theory, krill-based foods could be farmed more sustainably than fish, but in practice, most of the wild krill catch is fed to fish farms. If krill were more popular as a direct-to-human food, there might be more financial incentive to farm it rather than catch it wild.
Furthermore, you can't make blanket claims like "eggs are damaging to your health", because there are tons scenarios where that is untrue. Are eggs a bad dietary choice for someone who already consumes a high saturated fat, low fiber diet? Probably. On the other hand, eggs are an integral part of my diet and I would be much less healthy without them.
You should at least be honest about your motivations as a vegan. I don't care if you want to take a stand against subjugation of animals, that's fine, but don't try and sell the diet to people who don't share your feelings in that regard with health scare tactics. That's just plain lame.
Please cite any references which support this claim.
That being said, in addition to the anecdotal evidence that vegans are VASTLY under-represented in the upper echelons of strength and power sports compared with their relative abundance in the general population, there are some good studies comparing muscle protein synthesis following ingestion of whey vs soy protein:
http://jap.physiology.org/content/107/3/987.short http://ajcn.nutrition.org/content/86/2/373.short http://www.biomedcentral.com/content/pdf/1743-7075-9-57.pdf
There is also some data suggesting vegans have slightly lower free testosterone and free IGF-1 than omnivores too, though at the highest levels rampant steroid use probably makes this a moot point.
> There is also some data suggesting vegans have slightly lower free testosterone and free IGF-1 than omnivores too, though at the highest levels rampant steroid use probably makes this a moot point.
Again, you are using conjecture over peer reviewed research. Take a look at http://nutritionfacts.org/2013/02/12/less-cancer-in-vegan-me... if you're interested in actually learning the facts.
Finally, the down votes just serve my point. People rather bury their heads in the sand and pretend animal products have some magical effect on human health, especially in athletes, which is a true ode to powerful industry lobbying.
There's also something to be said for algae and algae oil, but it isn't likely to be useful until someone works out how to change its flavor to be more palatable.