Sharperiron and other blogs that really take issue with this term as if we mean that the gospel is all there is and the gospel is all that matters. They like to jump on the "Gospel Centered" proponents for being dismissive of other doctrines that are equally essential. My hunch is that they are really against the people that are making this stuff popular - people like Tim Keller and other Reformed types as a reaction against them because although they emphasize the gospel, they get other things wrong. So, the objection to "Gospel Centered" is really a reaction against "Gospel only". I really don't think that the Gospel Coalition and T4G guys are really promoting "Gospel only". Those critics who think they're more Biblically faithful like to say they are "Bible Centered" or "God Centered". All three terms are fine to use depending on what you mean by all of them.
God-Centered - all that a ministry does is for the glory of God to show forth the holiness and character of God. If this is true then you must be...
Bible Centered - all that a ministry does to glorify God is rooted in Scripture as it's compass and sole authority. Nothing is done without consideration to "what would God think of this?" Therefore: "What has God said about this?" However, to stop here is a mistake. What God has said about anything in Scripture serves an overarching theme and purpose for why the Bible was written. The Bible is not a church manual or a self-help book. It's a story. It's the story of God's redemption of man. Thus if you are going to be "Bible Centered" you must ask yourself - how does this thing we are considering find it's place in the Bible's overall story of the good news of redemption? Thus...
Gospel Centered - all that a ministry does to glorify God is rooted in Scripture so that it is faithfully declaring the story of Scripture: the gospel.
So, if someone is against a church being "Gospel Centered", I have to ask - Who is at the center of the gospel story? It's Jesus (who is God), therefore, if you think you're being "God-centered", then you will have to be "Gospel centered"! Who is the entire Bible about? Jesus! And what is the story of Jesus all about? The good news of His saving His people! The Gospel.
There are all kinds of gospel-less ministries that all claim to be operating under Biblical principles and Biblical authority. From the Apostolic, Pentecostal, full-4-square gospel legalist all the way to the KJV Only, suit and tie wearing, soul winning Baptists: they all claim to be "Biblical" but you'll seldom hear the gospel preached. You'll hear moralism. Oh yes, after the end of a ranting sermon on some pet peeve, the preacher will always give an invitation asking if anyone would like to "get saved"; they'll make reference to the death, burial and resurrection as if by merely mentioning these facts without any further explanation, they've been faithful in sharing the gospel. A Catholic believes in those things too, but it doesn't mean he understands or preaches the gospel.
Being Gospel-Centered means taking every text of scripture and explaining it's gospel implications and applications. There are no doctrines, Bible stories, Psalms, Proverbs or Prophecies that do not somehow garnish the overall gospel plot of the Bible and point to Jesus. If you simply preach from a Proverb to help someone learn how to get along with others better, then you might as well be preaching in a Synagogue or a Mosque. If you can't figure out how that Proverb which seems totally unrelated to the gospel, is the wisdom of God that leads a person to Christ for salvation, then you shouldn't be preaching at all - you have no good news, you have nothing to say. So, if you're boasting about being a Bible expositor and exegete, but there's no gospel woven throughout your exposition, you're blowing hot air.
I remember being rebuked by someone after I thought I had preached a faithful exposition and exegesis of a passage. I was told by a person who came with his unconverted wife, that I had failed to explain how that passage should bring his wife to an understanding of the gospel. As usual, I was offended at first and disagreed with him, but as I pondered on it, I began to see he was right. I thought I was being Biblical, but I left the gospel behind. I had failed. Without the good news being the center of our ministry, we lack "the power of God unto salvation".