Explain Psalm 34:14???

Psalm 34:14 how do you pursue peace? In v16 why is God against those who are evil, if we’re supposed to love one another as Christians? If this is a Psalm of encouragement, how could David have written it when he was pretending to be insane?

The first thing to remember is that 'peace' is not just the absence of conflict. It is a state or point in which stillness, rest, calm and tranquility are reached. God isn't saying, purse peace and protest war…war happens. There is a time and place for war. To pursue peace is to pursue a stillness with God.
In verse 16, is says, "the face of the LORD is against those who do evil" Beth picked Esther up from preschool. The children were on the playground. One boy went over to Esther, stuck his tongue out and said, "we don't like you." Beth stepped to that boy and said, "You don't talk to my daughter like that." Instinctively a parent comes to the defense of their children. God does the same thing. Most of the time 'evil doers' are doing evil to God's children…he simply is stepping in.
In regards to the insanity plea, have you ever been encouraged by a song or movie? If so then you have been encouraged by someone who may have been going thru a 'crazy' time or depressing time in their lives.