Why do children copy everything you do?
Because observational learning is one of the primary mechanisms by which humans acquire behaviour, and children are unusually strongly disposed toward it — to a degree that is genuinely distinctive among animals.
The classic demonstration. Albert Bandura's Bobo doll experiments in the 1960s showed children a film of an adult behaving aggressively toward an inflatable doll. Children who watched subsequently reproduced the specific behaviours, including novel ones they could not have invented — establishing that behaviour is acquired by observation without direct reward or punishment, which contradicted the behaviourist orthodoxy of the time.
Over-imitation, which is stranger and more revealing. Studies by Lyons, Horner and Whiten and others found that when shown a demonstration containing obviously unnecessary steps before achieving a goal, young children reproduce all of it — including the pointless actions — even when they can see the steps are irrelevant and even when told to be efficient.
Chimpanzees, tested the same way, skip the unnecessary steps. Children do not.
Why this apparently irrational behaviour makes sense. Human culture consists of practices too complex for any individual to derive from first principles — cooking, tool use, social convention, language. A child cannot tell which steps matter, and the safest strategy is to copy the whole thing faithfully and work out the reasons later. High-fidelity imitation is the mechanism that allows cumulative culture, and the apparent inefficiency is the cost of transmitting things you do not yet understand.
What this means practically:
They copy what you do, not what you say. Instructions compete with demonstration, and demonstration usually wins.
They copy incidental behaviour — how you speak to a call handler, how you react to spilling something, your phone habits, how you talk about your own body.
They copy people they identify with, and social status affects who gets copied.
Modelling is therefore a teaching method, not just a risk.