The business of the organization as "mother" is an older concept, but I remember it well even during the years I was an elder (1985 - 1995). Here are a couple of older quotes on the organization as "mother".
"If we are to walk in the light of truth we must recognize not only Jehovah God as our Father but his organization as our mother." The Watchtower, May 1, 1957, p. 274.
"After being nourished to our present spiritual strength and maturity, do we suddenly become smarter than our former provider and forsake the enlightening guidance of the organization that mothers us? ‘Forsake not the law of thy mother' (Prov. 6:20-23)." The Watchtower, February 1, 1952, p. 80.
The other reference that was popular was the organization as the ark. Here's a couple on that:
"7 Did Jehovah ever use more than one organization during any period of time? In Noah's day only Noah and those with him inside the ark had God's protection and survived the floodwaters. (1 Peter 3:20) Also, in the first century there were not two or more Christian organizations. God dealt with just the one. There was just the "one Lord, one faith, one baptism." (Ephesians 4:5) Likewise in our day Jesus Christ foretold that there would be only one source of spiritual instruction for God's people."- You Can Live Forever on Paradise Earth, p. 193
"17 Well, Noah built the ark with the help of his married sons, hence far less than a century before the deluge broke. So the ark building took place during the "time of the end" of that "ancient world." So we must look for something special during this "time of the end," a thing from which this present generation of mankind can benefit or take advantage of during the urgency of the times. By Scripture and fulfillment of Bible prophecy it has been well established that the "time of the end" of this present "world" began in the autumn of the year 1914, while World War I was raging. Noah's ark would therefore picture that provision for survival that God makes through Christ for his faithful worshipers as the fiery end of this system of things draws near. That divine provision is the spiritual paradise into which God has brought his faithful worshipers since the year 1919 C.E., in which they live as his people restored to his favor and under his protection." - The Watchtower, 11/1/1974, p. 667
The reason I tie the two of those together is their similarity to a statement made by Cyprian, bishop of Carthage:
He can no longer have God for his Father, who has not the Church for his mother. If anyone could escape who was outside the ark of Noah, then he also may escape who was outside the church." -- The Treastises of Cyprian, Treatise I, paragraph 6
Replace the word "Church" in Cyprian's statement with the word "organization" and you'd have pretty much what the WT says about the org. The JW organization has a lot more in common with the Catholic Church than they would like to admit.