There's no case to handle the odd numbers. Also, because of the funny implementation of nextInt(), it's not consuming the next line character when you input the max value.
Also, there is a much better method to print out odd/even numbers: use an if statement for even/odd, then iterate through all even/odd numbers up to max.
System.out.print("Enter The Max Value: ");
int max = sc.nextInt();
System.out.print("Which Value Do You Want To Display Even Or Odd?");
sc.nextLine(); // consume \n from above
String answer = sc.nextLine();
if ("even".equalsIgnoreCase(sc))
{
for (int i = 0; i < max; i+=2)
{
System.out.println(i);
}
}
else if ("odd".equalsIgnoreCase(sc))
{
for (int i = 1; i < max; i+= 2)
{
System.out.println(i);
}
}
else
{
System.out.println("You didn't enter even or odd. quiting.");
}