I've heard this saying many times from people who are very mediocre in their area of ministry and who, instead of either studying and practicing their way to a degree of skill or admitting to their own pride that this was simply not their area of giftedness, use this to say that God doesn't care if you are good- He makes you good. Laziness and/or hubris, in my opinion. Name one great musician, preacher, missionary, etc who did not work, practice, and develop their gifting along with being honest about what that gifting actually was.
I think that are two things at play here.
One, this is just another instance of the church's falling into a cultural weakness- namely, the idea that equal opportunity isn't enough- equal results should be the norm. The idea, too, that everyone is a winner and it is anethema to come out and gently tell someone that they really are very bad at something. It's sad, I think- encouraging people in areas where they want to be gifted, but are not, destroys their incentive to discover their real area of giftedness. In so doing, it can destroy their potential as well. I really do think that everyone has something to contribute to the body of Christ, and I love to see people discovering their true gifts and callings and operating in them! It is true, of course, that giftedness comes in differing degrees as well as in differing areas, but I really don't see a downside to honesty here. I also think it's pretty awful to pass your own inadequacies off on God to magically fix. (of course God can also call us to step out of our comfort zone and fill an immediate need, even in an area where we lack skill, but this to me is a world away from the sort of life calling/ministry/gifting/talent/career I'm talking about here)
Two, I think it also has to do with the idea that "everyone is called to ministry" means "everyone is called to an official role in the church." We are all called to interpersonal ministry in our daily lives, of course, but our "Area of Ministry" may mean preaching, teaching, music, bookkeeping or it may mean running a successful business and employing the needy, or it might mean being a kick-ass architect and designing things that reflect the creativity of the Creator, or being a clean cop who puts his/her life on the line to protect the innocent, etc. Not everyone is qualified/called to be the preacher/teacher/missionary/
Basically, I think that the the first reason that so many people seem to insist on official church ministry, even though they are mediocre in it at best, is that our culture decries honesty in personal evaluation. The second is that other ministries tend to be devalued. Being a worship leader is no more spiritual than being a gifted history professor, or artist, or adminstrator, or molecular biologist, or janitor, or nanny, or mathematician...etc, etc. Some giftings can be put to use in a typical church service; some can't. If we are really being the church, all the time, then should it matter?