Sticking around, to me, means that you stay with the mother of your children.
My uncle is involved in my cousin's life, but he didn't stick around -- he left her mother. My cousin has a father and a stepfather. But that doesn't change the fact that her father bailed on the family.
Yes, sometimes the mom throws the dad out of the house. Maybe that's what happened to you, or in a family you know. But that's the exception, not the rule. Societally, we've got a problem with fathers walking away. There's a saying that the best thing a father can do for his children is love their mother. I believe that.
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Zoloft Sickness