This question brings tears to my eyes. Children may get angry at or frustrated with their parents, and they may frequently test limits—but they don’t hate their parents. This question usually comes up when moms or dads have exhausted their coping skills, often due to stress or depression.
Some periods of normal child development are infamously trying. Many infants suffer from colic during the first three months of life, when they cry for hours on end and can’t be consoled. Toddlers universally go through a stage in which they hit, kick, or bite when they’re angry. Children at this age have no idea that other people can feel pain, and so they simply need to be removed from the situation until they are able to calm themselves down. Two-year-olds are notoriously demanding, but 3-year-olds can be even more so—and are better at expressing their demands. Of course, teenagers can be so sullen and angry that it’s a cliché.
If you find yourself typing this question into a search bar, please get help. A pediatrician or a mental-health professional can help figure out what’s going on. It’s important to realize that however you might feel at the moment—and whatever your child might yell at you—your children are incapable of hating you.