Normally, I don't link to my own sermons. But in this case, I'm going to make an exception. As a Baptist pastor, I wrote this sermon specifically to address this question - Why would God prohibit making graven images?
The upthrust of the answer is that images stick the thing of which the image is made in a fixed point in time. And, the truth is, that as humans change, our images need to change with us. Idols don't do that. But our perception of our God does. My image of parents is not the same image I had when I was 5. If it were, something would be seriously wrong.
Unlike Muslims, we don't have a prohibition on images per se - only on images that we would worship. The Seventh Ecumenical Council in particular clarified that images of Jesus weren't sinful - indeed, God himself had incarnated and taken an image.
The Cherubim on the Ark of the Covenant were decoration - indeed, they were only said to "adorn" the Mercy Seat. The Ark itself was not something to be worshipped, but rather the God who sat there. To have prohibited any adornment would have been to diminish from the grandeur afforded any monarch.
Christians may have images that remind us to worship, but we are specifically not worshipping the thing itself. Crosses and crucifixes can, incorrectly, be viewed as idols to the unitiated. But the theology behind it (again see the Seventh Ecumenical Council), is clearly not idol worship any more than a To Do application on my phone dictates my life or a telephone is the thing to which I talk. It may be a medium that reminds me, but it is not the thing in and of itself.
But to make an image of God specifically is an affront to his character and our own. By fixing an image of God, it becomes too easy for that to become our only image of God. And, no one image can capture the full magnificence of his splendor.
As an example, I have, on my desk, this picture I took of the Grand Canyon.
I took that one my way down. The Canyon itself hasn't changed in thousands of years, but as I walked, my perspective of it changed dramatically. The deeper I got, the more amazing it got. I can't give you one picture of the Canyon that captures its full essence - and no one can give you one picture of God that communicates his full majesty. We just aren't equipped for it.
This is God's motivation - he wants us to experience His fullness and not settle for a single image. As such, the prohibition on making his image isn't because he doesn't want us to imagine him at all - but rather because he doesn't want us to settle for limited scope. I can show you what Ganesh looks like. There are pictures of other "gods" that abound.
But the God that Christians serve is
"able to do immeasurably more than all we ask or imagine, according to his power that is at work within us.
... exchange the glory of the immortal God for images made to look like a mortal human being and birds and animals and reptiles (Romans 1:23)
then we know that our foolish hearts will be darkened (Romans 1:22) and that we become sinful and stuck. (the rest of Romans 1).
tl;dr> In short, the prohibition on images isn't for God's protection, but our own.