Be more specific about equality.
I will be honest based upon only my observance. Since times have changed when it comes to a parental role - man works, woman a housewife, there is not much support for the men who are playing the woman's role when it comes to raising a child.
There is not much support for single-fathers but the awareness is growing. A father who has to fight with everything he has to prove the child is better in his custody. Because even if the mother is unemployed, most courts still grant custody to them simply due to the mother is a better provider when it comes to nuture & growth. If a child is in the father's custody & the mother fails or is behind in child support payments, the punishment isn't as harsh as it would be for the father if role was reversed. & of course there are many similar situations like these.
I think this has the biggest gap where equality should be played. Everything else is just a race to see who is better.