Owning feelings does not mean letting a child do anything that he wants to do. We are talking about freedom to feel, not freedom to act. Respect for the child's feelings is part of respecting their integrity. Emotions well up spontaneously and are a part of all of us. To deny that emotions exist is both foolish and dangerous.
Denial can lead to later emotional problems and even to physical problems.
Unintentionally, we treat children like emotional computers into whom we try to program appropriate responses. If their feelings don't match ours, we tend to get irritated. But they cannot do this, anymore than we can. They have neither the power to manufacture nor suddenly turn off their feelings. Our job as parents is to teach children to acknowledge their feelings and then learn to control their actions.