How should I understand the emphasis on "begotten, not made" in the Nicene Creed? I'm trying to understand the importance the repetition of &quot;begotten&quot; in the Nicene creed. It states (emphasis mine):

We believe in one Lord, Jesus Christ,
    the only Son of God,
    eternally begotten of the Father,
    God from God, Light from Light,
    true God from true God,
    begotten, not made, one in Being with the Father.

I understand the purpose of this: that Jesus is the Son of God, that He is wholly divine, and not a separate entity from the Father, but I'm not fully clear on the purpose of emphasizing the difference between begetting and making after stating it once already.
The Catechism of the Catholic Church explains the emphasis to combat early heresy that Jesus's divinity was adopted, not inherent:

But already in the third century, the Church in a council at Antioch had to affirm against Paul of Samosata that Jesus Christ is Son of God by nature and not by adoption. The first ecumenical council of Nicaea in 325 confessed in its Creed that the Son of God is &quot;begotten, not made, of the same substance (homoousios) as the Father&quot;, and condemned Arius, who had affirmed that the Son of God &quot;came to be from things that were not&quot; and that he was &quot;from another substance&quot; than that of the Father.

Based on this, I read the emphasis merely as a way to ensure people know that Jesus is one with the Father: &quot;we really mean the same entity, not someone or something else.&quot;
But, C.S. Lewis in Mere Christianity puts it thusly:

We don't use the words begetting or begotten much in modern English, but everyone still knows what they mean. To beget is to become the father of: to create is to make. And the difference is this. When you beget, you beget something of the same kind as yourself. A man begets human babies, a beaver begets little beavers and a bird begets eggs which turn into little birds. But when you make, you make something of a different kind from yourself. A bird makes a nest, a beaver builds a dam, a man makes a wireless set—or he may make something more like himself than a wireless set: say, a statue. If he is a clever enough carver he may make a statue which is very like a man indeed. But, of course, it is not a real man; it only looks like one. It cannot breathe or think. It is not alive.
Now that is the first thing to get clear. What God begets is God; just as what man begets is man. What God creates is not God, just as what man creates is not man.

I read that as a limitation of God's power: that He is incapable of creating something that is of Himself, He must beget it.
How should it be read? That it's merely a linguistic tool to emphasize Jesus is one with the Father, a limitation on God's power to create, or something else?
The Arians were very good at using the same (Biblical) language as orthodox Christians, but meaning entirely different things by them. The language in the Creed had to be so specific that it removes all wiggle room. I think I can hear, in the creed, the frustration of someone so upset with Arian double-speak that they pound orthodoxy home with some conceptual overlap. 

Nevertheless, the two statements do affirm different things about Jesus:


  eternally begotten of the Father


That is, the Son is eternal. He was not begotten at some point in time, and there was not a time when he did not exist. But this does not mean, by itself, that Jesus was the same type of being as God.


  begotten, not made


Here I think your C.S. Lewis quote applies. Jesus is not a creature, he is not part of the creation. Contra the Arians, begotten does not mean created. The other clauses (true God from true God, one in Being with the Father, etc.) explain what it means to be begotten as distinct from created.