In the case of milk and eggs, it goes beyond "taking advantage" of animals. When egg-laying hens are bred, half the chicks are male (thus non-productive). Those male chicks are ground up alive or left to die in dumpsters. The females go to live in cramped, dirty conditions. They've been selectively bred to produce an unnatural amount of eggs, which depletes their bodies of needed nutrients, so generally they have poor health. They have their beaks cut off without anesthesia. They are usually put through periods of starvation to cause 'forced moulting'...something about this makes them produce more eggs. Then they are killed at a small fraction of their lifespan when their production begins to slow down.

Similar case for milk; cows have to be impregnated to produce milk, so when they give birth, their calves are taken away immediately. Usually they become veal, or if the calf is female, becomes a dairy cow like her mother. Cows go through back-to-back lactation cycles for a few years, and then get killed when their milk production slows down. Again, they are bred (and given hormones in some cases) to produce way more milk than what is healthy for their bodies to give, and are often kept in bad and stressful conditions.