But, I noticed a change in him when me and my husband broke up
Jay was only 12 when his father left home without providing a reason (which Jay later found out was because of the anonymous murder of his uncle on the street that drove his father insane in persuit of finding the killer that he became an alcoholic and left home). At that point Gloria Carter was left a single parent raising Jay and his siblings. And as any other person that has gone through divorce knows, the kids, especially those at a younger age, are most affected by it and you will without a doubt start to see changes in their behavior after the parents separate.
To help improve the meaning of these lyrics, visit "December 4th" by Jay-Z Lyrics and leave a comment on the lyrics box