SAS else if clause confusion

I'm running the following code:

data new;  
set old;    
    if visits=. then band='Poor';  
    else if visits=1 or visits=2 then band='Low';  
    else band='High';  
run;

My confusion is when the else if statement is changed to:

else if visits=1 or 2 then band='Low';

Why does the value Low appear as the band for cases where visits are greater than 2 instead of High?