Why? I have stayed put during a category 4 hurricane and survived just fine. A little prep-work, some extra supplies, basic survival skills and helpful neighbors can make the experience ... tolerable.
If your house is of modern construction, don’t live in a floodplain, don’t live in the storm surge area, your house is not threatened by falling trees, you have enough food and water for 30 days and have a working generator with fuel supplies, you are most likely going to be just fine. Board up the windows, store some water, make sure the chain saw works, sandbag the entrances where water might get in.... basic stuff.
Conversely, if any of those exceptions DO apply to you, best to bug out. But make sure that you take identification, extra money, extra clothes and important papers. Still board up and lock the house. Put the valuables away, etc. Evacuation can be EXTREMELY stressful. Bugging out if you don’t have a place of safety to go to or don’t know what to bring with you, can often be a bad idea.
Media hype aside, we (Americans) have survived hurricanes for many many years.
Get the kids out of there. It is that simple.