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One of the most prevalent fallacies in human development is the idea that if you respond attentively to your young children, it will form them into weak self-centered dependent adults.
The research indicates the exact opposite. When children experience emotional attunement and responsiveness from their caregivers it helps them feel safe, which in turn helps their brain develop more awareness and complex focus in relationships. When children's emotional needs are ignored, they develop heightened fear states that make it hard for them to learn the nuances of relationships. (check out the strange situation studies, and Es Tronick's Still Face Experiment, and the Adult Attachment Interview, and all the longitudinal studies done with all three tools).
You aren't spoiling your child when you comfort them, hold them, respond to them, and treat them with the same respect you would want in a difficult or need based moment.
Ignore the judgment and follow your instincts for care. I promise you won't regret it.
In this video, the speaker discusses "Compassionate Transportation," a technique for safely and empathetically getting children to cooperate when they are overwhelmed by emotions and immediate actions are necessary.
The myth that comforting your child will "spoil" them is not only emotionally harmful but also creates an altered brain state that leads to higher levels of stress and mental illness in adulthood, giving them compassion and comfort will only help them develop a healthier brain function.
In this video, learn about the power of empathy when dealing with anger, but also be warned about the limits of empathy in the context of abusive mentalities, where anger is used to justify harmful behavior.