Eating eggs is not murder, nor it is eating meat. Eating eggs can be okay for a vegetarian.
The eggs that we eat are not fertilized, and therefore are not unborn chickens. The chicken eggs that you get at the grocery store are basically the same as the eggs that come out of a woman’s ovaries. Regardless of what stage of development an embryo is considered to be a person, even most die-hard pro-lifer would not contend that an unfertilized egg is a “life”, so there is no moral or ethical problem with eating eggs; at least not in that way.
The problem with eating eggs comes not from the eggs themselves, but the horrible, cruel torturous treatment that the chickens who lay the eggs are given. The eggs that you buy in the grocery store usually come from factories (the modern day “farm”), where countless chickens are locked in tiny steel cages that are not big enough for the chicken to even turn around in. The cages are piled high (causing the chickens to urinate and defaecate on each other depending on the cage design), in either continually dark or lit warehouse to trick the chickens into constantly laying eggs. Their beaks are often cut in half as well to prevent them from pecking at themselves or each other. And it should come as no surprise, that once a chicken can no longer produce good eggs, its retirement package is a trip to the slaughterhouse. Even worse than all of that is the fact that because only females can lay eggs, the farms factories have no use of males chicks, so they have all of the adorable little yellow baby chicks move by on a conveyor belt while inspectors check their cloacas to sex them, letting the females pass, and throwing the males in a literal SHREDDER! Imagine if aliens came down and started throwing human babies and children into a shredder. 😒
This is the reason to not eggs.
That said, if you can source your eggs from a real farm, specifically a “free-range” farm where the eggs are hand-picked by a presumably caring farmer from chickens who are treated well, fed well, allowed to frolic on the grounds, and basically given a proper and happy life, then there is no reason not to eat eggs. Eggs are a “power-food”, and it has been shown that eggs from “happy” chickens who naturally lay eggs instead of being forced, are better tasting and more nutritious.
Unfortunately because of the unending increase of the human (over-)population, true farms where animals are given personal attention are just not feasible. To provide for the never-ending human demand, many farms had (and still have) to sell out to large firms who convert to factories to mass-produce meat, eggs, and milk. That’s why it is the same story for milk; not only is getting milk from a cow not murder, but it can actually help the cow to remove excess milk once its calf has ceased nursing. However that only works for hands-on farms, not factories where cows are locked in a tiny stall, hooked up to machines that suck them dry non-stop, until they can no longer produce good milk, then the cow is shipped off to the abattoir.
So try to find a real farm, (or even consider making your own; you don’t have to have a big one with lots of animals) because you can have eggs and milk without the guilt, plus you would be helping the farmer—of course if too many people go to a single farm, then the farmer might end up having to “factory-ize” to provide the excess demand. (Alternately, it would be much easier if everybody just stopped having kids for a couple of generations; if the human population were—much—lower, everything would be easier.)