Why can't I use 'continue' inside a switch statement in Java?

Falling through is the standard behavior for a switch statement and so, consequently, using continue in a switch statement does not make sense. The continue statement is only used in for/while/do..while loops.

Based on my understanding of your intentions, you probably want to write:

System.out.println("default");
if ( (a == 'a') || (a == 'b') ){
    System.out.println(a);
}

I would also suggest that you place the default condition at the very end.

EDIT: It is not entirely true that continue statements cannot be used inside switch statements. A (ideally labeled) continue statement is entirely valid. For example:

public class Main {
public static void main(String[] args) {
    loop:
    for (int i=0; i<10; i++) {
        switch (i) {
        case 1:
        case 3:
        case 5:
        case 7:
        case 9:
            continue loop;
        }

        System.out.println(i);
    }
}
}

This will produce the following output: 0 2 4 6 8

The continue-Statement may be used in loops and not in switch. What you probably want is a break.

Because you have a continue outside of a loop. continue is for jumping back to the beginning of a loop, but you don't have any loop in that code. What you want for breaking out of a switch case block is the keyword break (see below).

There's also no need to put every case block within braces (unless you want locally-scoped variables within them).

So something a bit like this would be more standard:

class swi22
{
    public static void main(String[] args)
    {
        int a=98;
        switch(a)
        {
            default:
                System.out.println("default");
                break;
            case 'b':
                System.out.println(a);
                break;
            case 'a':
                System.out.println(a);
                break;
        }
        System.out.println("Switch Completed");
    }
}

There's also a school of thought that says the default condition should always be at the end. This is not a requirement, just a fairly widely-used convention.