The eggs you buy from a store in the west aren't fertilized. Males are removed so this doesn't happen. Some areas, like in China, do serve fertilized eggs. You can watch the idiot abroad series where the main guy goes to China for an example of this. The eggs you eat are equivalent to a woman's period, but more appetizing, unless you're into that, no judging.

A major issue with commercial farming is efficiency. Milk and eggs provide regular income, but half of those born don't produce it. Male chicks are thrown in a grinder, and male calves become veal. A chemical in the stomachs of those calves is also what is traditionally used to produce cheese. You can't get from adult cows.

For animals grown primarily for meat (which includes broiler chickens, and cows like the Belgian Blue) they have been genetically modified (through artificial selection and insemination) to produce as much meat as possible. Broiler chickens' muscle grows 4 times faster than they did 100 years ago, and have the medical issues that come with it, such as organ failure and skeletal problems. Walking is often very painful if even possible. There have also been other things done like cutting the tips of beaks to limit birds pecking each other when crowded.

Many farm animal breeds are very different from their origin, even from the same breed 50 years ago, with less efficient versions and breeds becoming extinct. Same occurs with plants people farm. Some of these animals can no longer survive in the wild (if much at all).

There are some communities which limit animal consumption to local goat milk and chicken eggs, where they can be assured of how they're raised and treated. There are also people who hunt and eat that meat, but won't buy store-bought because of the difference in the animal's life. How an animal's treated matters a large amount.

You're right that cats are (obligate) carnivores. Even some common cat food brands aren't great for them as they contain plants and cats suck at digesting plants. They do have nutritional needs such as particular organs, and can still benefit from supplements.

Dogs are omnivores, and one of their genetic differences from wolves is that they're quite good at breaking down starch. They have similar nutritional needs and capabilities to humans. Like humans there are some things they can't produce in enough quantity or at all, and need to get it externally. This means they need to eat plants. Also like humans, while they can produce enough collagen, it's only just enough, and only with the proper nutrition, so unless they have a very rare allergy, they should at least eat some animal products, even eggs, to ensure they meet their nutritional needs.

Anyone with a pet should really learn what they need, and only get one if they can handle that, diet and otherwise. Even rodents have special needs, like things to chew on to wear their ever growing teeth down.