Why use MAX232 when using USB-to-Serial cable
A USB to RS232 cable is supposed to output around -12V for the 1 state and around +12V for the 0 state. Your particular cable might be cutting a few corners. For proper compatibility, you need to use the correct chip. However, if you are building a one-off prototype with a specific cable, then you may be able to get away with hacking something together that does not use the correct interface chips. You may run to unexpected issues, though.