Что я делаю не так?

package com.javarush.task.task09.task0915;

import java.io.CharConversionException;
import java.io.IOException;
import java.nio.file.FileSystemException;

/*
Перехват выборочных исключений
*/

public class Solution {
    public static StatelessBean BEAN = new StatelessBean();

    public static void main(String[] args) {
        try {
        handleExceptions();
        } catch (FileSystemException e) {
            BEAN.log(e);
        }

        }

    public static void handleExceptions() {
        try{
            BEAN.methodThrowExceptions();
        }catch(FileSystemException e){
         BEAN.log(e);
         throw e;
        }

        catch(CharConversionException e) {
         BEAN.log(e);
        }

        catch(IOException e){
         BEAN.log(e);
        }


    }

    public static class StatelessBean {
        public void log(Exception exception) {
            System.out.println(exception.getMessage() + ", " + exception.getClass().getSimpleName());
        }

        public void methodThrowExceptions() throws CharConversionException, FileSystemException, IOException {
            int i = (int) (Math.random() * 3);
            if (i == 0) {
                throw new CharConversionException();
            } else if (i == 1) {
                throw new FileSystemException("");
            } else if (i == 2) {
                throw new IOException();
            }
        }
    }
}