In Calvinism, why does free will to accept salvation seem to take away from God's glory?

With my understanding of Calvinism/Reformed theology, the question here is confused on what the theology actually teaches. My understanding is that you are unconditionally selected for grace, however, once that grace is poured out on you, you freely and willingly surrender to it and follow God. I find this is a common misunderstanding. Common enough that I've had to bring it up twice in other answers 1 2.

With that, I would answer that free choice is part of the process all along, so the question is averted.

However, perhaps you mean sovereignty rather than glory. The question makes more sense if you ask "Why does free will diminish God's sovereignty?" To many Calvinists, free will, defined as total human sovereignty over their own choices, does diminish God's total sovereignty. In Calvinism, nothing happens that God did not decree or make certain. This appears to stand in opposition to free will, where you essentially save yourself, proving that God is not wholly sovereign, and this does, by extension, rob God of the glory he'd normally be due for the power of his saving grace.

What may be particularly illuminating on this issue is the book Calvin vs. Wesley: Bringing Belief in Line with Practice by Don Thorsen. I have not actually read it, but the nuanced differences between these theological fathers can be previewed on Google books, though it does favor Wesleyan theology. Wesley stressed both God's sovereignty and human free will, standing in contrast against Calvin, who seems to stress God's sovereignty and trivialize human free will in his writings. Like you, Wesley saw no reason why free will should threaten God's sovereignty.

However, I'm having trouble finding a Calvinist who argues their theology the way you portray it in your question. Which takes us back to the first part of this answer. Free will is present in Calvinism, however they generally don't want to use the term because of the confusion over what they would mean by it, instead preferring things like "man acts out of necessity, but not coercion" or "libertarian freedom". In Calvinism, you do freely and willingly choose what has been made certain by God's sovereignty.

The reason freely choosing to accept the gift of Jesus would rob God of glory in Reformed theology is that it would soft pedal the nature of the fall. Calvinists understand that when mankind fell into sin it affected our entire person and nature, leaving no portion unaffected. This is not the same thing as saying that humanity is as bad as it could possibly be. We do have choices, and God bridles evil as a matter of common grace, but that every part of man has been corrupted by the fall: our thoughts, our consciences, our bodies, our emotions, our reasoning, our spirituality, and everything else that makes us human is worse than it was before we sinned, but we have enough of the general idea behind the thing that we can recognize what we are missing.

The phrase, "pulling yourself up by your bootstraps" has lost its rhetorical effect due to common usage in situations where helping yourself is merely challenging and not impossible, but the literal imagery is someone doing something physically impossible but conceptual feasible for someone who does not understand physics. We are familiar with the experience of pulling on something heavy and lifting it up, so we can imagine a person who is really strong being so strong he can lift his own weight and pull himself out of a pit by pulling on his bootstraps. But to explain in precise physical terms why that can't happen takes some effort.

In the same way, "choosing Jesus" with no special grace or election in the Calvinist conception is virtually the same as pulling oneself up by their own bootstraps. It seems possible, but in order for it to happen it would have to mean that a person who is enslaved to sin one day decides for themselves that they've had enough of it and don't want to be a slave. What then is slavery if you can just walk away from it? It means that a person who decides to sin because of a mistrust and growing enmity with God decides one day that God is now trustworthy again and a friend.

The free-will emphasis ultimately takes the work of God in planning, urging, sending, entreating, disciplining, electing, and regenerating and attributes it to the person who is not responsible for it. Jesus died on the cross to accomplish this, and it was the Father's will from the foundations of the world to bring about salvation for his people this way and his primary method of glorifying his name. To undercut the divine action and attribute it the the sinner gives the credit to the sinner for doing the thing that God did, which robs him of glory.

When the Israelites made the Golden Calf they said, "These are the gods that delivered us out of Egypt," and in so doing attributed the salvific work of God to inanimate idols and thereby robbing him of glory. God makes a name for himself by dealing mercifully with and saving his people, so Christians in turn are to ascribe to the Lord honor for his mighty deeds; the greatest of which is saving sinners.