Here's the quick and dirty version. If it's interesting to you I can direct you to the longer, more researched, more eloquent, better, version when it's ready.
Binding of Isaac is a phenomenal game for many reasons. However, what I find most interesting is the narrative and the way it works with the gameplay to tell a very intriguing story about human nature. Isaac is, quite obviously, a child. A child that is nearing the age of puberty.
The initial disconnect between Isaac and his mother is one of extreme religious disconnect. Isaac has reached the age were he has begun to form his own thoughts and opinions about the world, and, as one might suspect, it does not agree with that of his mother's. This is something that most anyone can relate to. We all experience the alienation from our parents as we begin to grow and question everything they have taught us. This leads many youths to search for their own meaning, through video games or friendship or just isolation from their parents. This is the metaphorical, and perhaps quite literal, basement. How common is the story of the teenager spending all their time in the basement doing whatever it is, alone, or just away from their family?
As the story continues we see Isaac slowly grow from prepubescent child, afraid of spiders and bugs and simple, instinctual fears, into the isaac at the end of the game; his fears are much more modern, adult.
I believe the procedural generation plays into this very well. It says to the player, to the child that is coming of age, that there are an infinite number of paths you can take to reach the potential of who you are. Any different combination of items or friends or techniques you learn along the way, can lead you to the ultimate goal of realizing who you truly are as a person. Whether it be through acceptance of your own original sin, if you follow religion, or destruction of one's own self, quite literally, and becoming who you are and not who your mother or anyone else thinks that you should or could be.
That's the quick and dirty for now. I do promise a more complete, researched, in-depth essay at a later date. Thank you for reading, and I hope it was enjoyable.