This writes all of the strings to the screen every time pin 2 is HIGH.
No, it doesn't. It writes all of the strings to the screen while pin 2 is HIGH.
First, it appears that you want to write one string per switch press. To do that, you need to do two things. One is that you need to detect the transition from released to pressed (or from pressed to released). To do that, you need to keep track of the previous state of the switch. When the current state is not the same as the previous state, a transition has occurred. The current state (pressed or released) will tell you which kind of transition has occurred.
The second thing you need to do is count the number of transitions of the correct type that have occurred. Use that count as an index to print the nth string, rather than using a loop to print every string. Reset the counter to zero when it exceeds the number of strings.