bash argument case for args in $@

You can allow both --a=arg or -a arg options with a little more work:

START_DATE="$(date '+%Y-%m-%d')";
LAST_DATE="$(date '+%Y-%m-%d')";
while [[ $# -gt 0 ]] && [[ "$1" == "--"* ]] ;
do
    opt="$1";
    shift;              #expose next argument
    case "$opt" in
        "--" ) break 2;;
        "--first" )
           START_DATE="$1"; shift;;
        "--first="* )     # alternate format: --first=date
           START_DATE="${opt#*=}";;
        "--last" )
           LAST_DATE="$1"; shift;;
        "--last="* )
           LAST_DATE="${opt#*=}";;
        "--copy" )
           COPY=true;;
        "--remove" )
           REMOVE=true;;
        "--optional" )
           OPTIONAL="$optional_default";;     #set to some default value
        "--optional=*" )
           OPTIONAL="${opt#*=}";;             #take argument
        *) echo >&2 "Invalid option: $@"; exit 1;;
   esac
done

Note the --optional argument uses a default value if "=" is not used, else it sets the value in the normal way.

Use shift in the end of each case statement.

Quote from a bash manual:

shift [n]

The positional parameters from n+1 ... are renamed to $1 .... Parameters represented by the numbers $# down to $#-n+1 are unset. n must be a non-negative number less than or equal to $#. If n is 0, no parameters are changed. If n is not given, it is assumed to be 1. If n is greater than $#, the positional parameters are not changed. The return status is greater than zero if n is greater than $# or less than zero; otherwise 0.