We will always fail on our own?

The Myths
"We will fail every task we attempt on our own."
OR
"Non-Christians cannot do any good works."

The Reality
Any non-Christian can tell you that those statements are bogus. There are plenty of people who don't trust in God, but are able to accomplish all kinds of things successfully.
The follow-up argument I've heard sometimes is that if you are able to accomplish something, it won't be satisfying. Lance Armstrong, Bill Gates, and many others have not only accomplished impressive tasks, but done good works, which I'm certain they could honestly say have brought some level of satisfaction.


Why It Matters
Rather than try to differentiate ourselves from unbelievers by making false claims about what they can or can't accomplish, or judging their motives or level of satisfaction, we should instead recognize that the principles that lead to satisfying accomplishments are God-given principles. Hard work and perseverance pays off, and good works are rewarding.
There are many natural blessings that come from following Godly advice, even for those who don't follow God completely. I think of it as a taste of the lasting satisfaction that comes from being fully devoted to God.
What's important is not whether  we can succeed in accomplishing anything on our own. What's important is recognizing that what we can't accomplish on our own is salvation and fellowship with God. It's important to recognize that our good works don't purify us from our sins and depravity; only God can do that.