"Coming in the opposite spirit" means you see something evil, but instead of railing against the evil thing, you pray for the good and holy thing to take its place.
When we intercede, we come in the opposite spirit.
For example:
When you see someone fighting against lust, you pray for them to have a spirit of purity.
When you struggle with fear, you ask God to fill you with His perfect love, which casts out fear.
If you see someone who is lukewarm toward God, you ask God to fill them with holy fire and passion for Jesus Christ.
There is an unholy substitute for every holy thing, but we don't focus on the unholy thing because we can't afford for it to fill our horizon. What you focus on you empower, and we never want to empower the work of the enemy in our lives.
So when we pray, meditate, and speak, we want our thoughts, prayers, and words to be filled with the good and holy thing that GOD wants to do.
That's why the apostle Paul wrote in Philippians 4:8, "Finally, brethren, whatever things are true, whatever things are noble, whatever things are just, whatever things are pure, whatever things are lovely, whatever things are of good report, if there is any virtue and if there is anything praiseworthy—meditate on these things."