Moving closer to Truth

Science classes in grade school taught a distilled version of the "scientific method" which consisted of a few steps:
  1. Generate hypothesis
  2. Test hypothesis
  3. Evaluate results
  4. Hypothesis confirmed or rejected
  5. Repeat
The thing I have forgotten about is that in science, one moves closer to Truth by seeking evidence that is contrary to the hypothesis.

This is often the exact opposite in the world of religion.  We tend to think we are moving closer to Truth by seeking evidence that supports our hypothesis.  That is we have an experience then we look for other things to support our interpretation of that experience.  Protestant Christians generally seek out some supportive Scripture.  

What we Christians are not very good at is entertaining and seeing evidence to the contrary to our claims.  Much of our time is constantly supplying evidence that only supports our claims.    

Perhaps a way to move closer to the way non-theists see the world is to begin to invert the way we seek to "justify" Truth.  Instead of constantly giving more and more supportive "evidence" to a truth claim, what would it look like to seek out contrary evidence? 

What would it look like to see this evidence to the contrary and use that evidence as a starting place for a conversation?  

Jesus was a guy who provided evidence to the contrary understanding of the truth claims of the religious authorities of his day.  

"God says do not work on the Sabbath." - Truth claim of authorities

"Should we not pull our donkey out of the ditch and save it's life even on the Sabbath?" - evidence to the contrary by Jesus.

"Well perhaps we do not sully understand God's desires for Sabbath." - responsible response of authorities 

"Jesus is an a-hole and we should kill this guy." - popular response of authorities