Here’s my take on this as it strikes close to home. While going through my divorce I was struck by the amount of bias the court system has against the father, from the attorneys straight up to the judges. With out going into details, my ex wife was/is not a suitable person to raise children. Despite the obvious, I had to fight tooth and nail to gain custody of my children. Even with evidence to the contrary, she was very close to winning custody. That would have been a grave mistake on the part of the Family Courts.
I prevailed and won custody but it was touch and go for a while.
Fact is the father has to work twice as hard to win a custody case.
I have had custody of my children for almost 8 years now (2 girls, 12 and 16).
I would challenge anyone who claims that a male can’t be as nurturing and caring as a female. I know of quite a few fathers who have custody of their children and the children are just as well adjusted as those raised by a mother.
When faced with the prospect of raising one’s children on their own, a PARENT, be they male or female will step up to the challenge. The MYTH that a male is less nurturing is just that…a myth.
So, my answer to the question is, Yes, a father should have every right to win custody of their children and gender should play no part in the decision.

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"If you don't know where you are going, you will probably wind up somewhere else."
- Laurence J. Peter