The eye of the storm is an idiomatic expression that means to be in the middle of a greatly argued or debated situation. It is commonly used to refer to any subject of much animated discussion/debate.
That the "eye of a storm is a peaceful place" is a meteorological nicety. As a fact, it offers little solace in real life. Even if it were safe, by the same meteorological token, a storm is usually a moving (non-stationary) force, so the so-called 'safe zone' would be 'safe' for no more than a brief period! Here's the excerpt from the Wiki page.
Though the eye is by far the calmest part of the storm, with no wind at the center and typically clear skies, over the ocean it is possibly the most hazardous area. In the eyewall, wind-driven waves are all traveling in the same direction. In the center of the eye, however, waves from all directions converge, creating erratic crests which can build on each other, creating rogue waves. The maximum height of hurricane waves is unknown, but measurements of Hurricane Ivan, when it was a category four hurricane, estimated that waves near the eyewall were in excess of 40 meters (130 ft) from peak to trough.
A common mistake, especially in areas where hurricanes are uncommon, is for residents to wander outside to inspect the damage while the eye passes over, thinking the storm is over. They are then caught completely by surprise by the violent winds in the opposite eyewall. The National Weather Service strongly discourages leaving shelter while the eye passes over.