Since you asked for comments on the "logic" of this article, I thought I would respond.
"Logic" refers to identifying the structure of arguments, and to assessing the strengths and weaknesses of arguments in terms of the relationship between premises and conclusions.
The article in question is full of the typical informal fallacies that are found in political and social discussions in popular media, both liberal and conservative. This article starts off with a fairly blatant "ad populum" fallacy that blames the blurring of gender roles on the twin evil forces of education and entertainment. It goes down hill from there.
The core of the argument is the appeal from the assumption that gender roles are natural to the conclusion that blurring gender roles will lead to a decline in the family and that a decline in the family will lead to a decline in society. This is not a very original argument and is the basic argument of the "family values" conservatives.
The fundamental assumption of this argument is that gender roles are natural. Religious writers such as the author of this article put this in terms of gender roles as made by God, not by men. No evidence in support of this assumption is given other than a quote from scripture. Since the article is addressed to fellow believers, this is all the evidence this author deems necessary. For anyone else it is an example of the fallacy of appeal to irrelevant authority.
The assumption about gender roles manages to confuse gender roles with sexual orientation and with work roles. This is an example of the fallacy of ambiguity.
This ambiguity is crucial in the next step of the argument, making the connection between the breakdown of gender roles to a breakdown in the family. The unstated assumption here is that the family is an arrangement between a biological male and a biological female for the purpose of procreating children. The argument attempts to conclude that blurring of the differences between men and women will threaten this arrangement. This is an example of the slippery slope fallacy.
Finally the argument wants us to think that a breakdown in the "traditional" family will lead to a breakdown in society and to the general decline of "Western Civilization". Family structures do reflect changes in social structure. In the times of the Hebrew prophets, society was agricultural. Among nomadic herdsmen, like Abraham, a patriarchal and polygamous family structure fit the social and economic structure. With the emergence of a more settled agricultural society, the family structure changed to a monogamous family. Industrialization further changed the family structure to account for the separation of economic work activity from domestic activity. The post industrial economy is now changing contemporary family structures. Note that changes in society bring changes in the family. To argue that changes in the family cause changes in society confuses cause with effect. The technical name for this is the fallacy of "non causa pro causa".
The argument does have a structure. And it commits fallacies at just about every step.
