We as fathers are reflecting who God is to our children. Since the birth of our child, they see us as the final authority in the house. We do not have the option of not reflecting who the heavenly Father is. My first concept of God was my earthly dad. That means when my dad is loving, I see God as loving. When my dad breaks a promise, I think that the God I pray to can also break promises. I was naive at that time but that was how I process things when I was a kid. It might be theologically wrong, but earthly fathers are theological primers for their kids.
We as fathers need to understand that there is a biblical pattern and mirroring when we father our kids. Our children also has a self will that wants to reject us as fathers thus there are times of rebellion but on the same breath we as dads have a childlike dependence to want to love the child despite the rebellion. As what Douglas Wilson said in his book Father Hunger: Why God Calls Men to Love and Lead Their Families,
Children need to be fathered despite their resistance, and they want to be fathered, and the ratios between those two sentiments vary. A wise father studies those ratios and works with them. That is why fathers need to learn how to be strict in the same way that God the Father is strict, and to be merciful in the same way that He is merciful. If we are strict only, we crush the spirit out of our children, or we provoke rebellion. If we are merciful only, we create a culture of entitlement and self-indulgence in the home. And, in the worst possible combination, if we are strict where God is merciful, and merciful where God is strict, then we are busy supplying the strip clubs of the future with all their pole dancers, and customers.