The simple answer to this is, NOTHING.
I spent most of my life thinking it was a globe and I'm at the not so naive stage now, so there's absolutely nothing that can convince me that the earth is a globe, either rotating or stationary.
The reasons are very very simple.
It makes absolutely no sense whatsoever. It only makes sense when your brain is saturated into believing what you are told to believe, not asked....TOLD.
To not be allowed to alternatively think and be ridiculed if you do alternatively think, by society, I think that alone should tell anyone that these things need to be questioned.
If I was backed into a corner and asked to name one thing that COULD, POSSIBLY sway me, I'd say viewing a rocket launch with all the equipment necessary to personally see the rocket launch with real astronauts inside of it and for that rocket to be tracked PHYSICALLY, by me, right into space.
If I saw that, I would probably change my mind.
Will I ever get that chance? NOT A CHANCE!