So much has changed over the past three or four decades in relation to the parents who are able to work from home, those who work as single parents, and those who have to provide the primary income for the family.
We know that the 21st century has a great deal of advancement already made toward the Gig Economy and the role of the entrepreneur in the economy. Things are definitely not as traditional as they once were back in the middle of the 20th century. The family situation needs to be re-evaluated.
It was hard to see the argument of women who wanted to say that the statement of a parent at home automatically indicates that it is the mother. Whether this is the part of a marriage or a single parent, with technology today, there is no reason to fear this topic due to the fact that men traditionally make more than women for the same positions in the workplace. Anyone can work outside the office, from the home or telecommute in general, providing the option for the father to stay at home with the ability to reduce the cost of childcare for every family. 
With the ability of a father living after the death of a wife, a divorce, or other tragedy that may require more care for the home and family, there is no reason to ignore the appreciation that these men deserve for their efforts. No doubt single and stay-at-home moms should be appreciated for that job as well, both men and women equally, but this should not be something that is considered as an argument that is playing out as an argument against women. Either parent has the right to make this decision and make the home one of love for all inside it.