Trump over played his hand because he's impulsive.Former Assistant Director for Counter Intelligence on MSNBC said for them to open up that type of inquiry into the POTUS, they needed detailed intelligence to validate a reasonable suspicion and it would have needed to be approved by DOJ. So Rosenstein approved of it.
This may be why Rosenstein appointed Mueller. Rosenstein seems like the type to think 10 steps ahead. Master chess player.