"and [you] are in no way frightened by your opponents.  For them this is evidence of their destruction, but of your salvation.  And this is from God."

To understand this sentiment, we must understand Jesus' words in John 12:43, "They loved the praise of men more than the praise of God." 

Here, in Philippians 1, Paul contrasts two groups of people:  Those who are still contending for the faith of the gospel (verse 27) and those who oppose the gospel.  See, those who fight for the gospel (those who have the gospel as a weapon), understand where their strength comes from.  This is why they are not intimidated by the opponents of grace.  They are confident. 

Paul lists one defense mechanism - being frightened.  I believe this verse applies to many defense mechanisms.  Those who do not use sarcasm with your opponents, or those who don't flee from your opponents, or spit insults, or make fun of, or yell at, or fight your opponents...

This produces evidence.

He who knows the Strong One does not need to fight to spread the gospel.

So, what is from God?