That is not a flaw of the phone. When your line is busy because you are talking, another caller cannot get through. Therefore your answering machine will never get the call.
The reason why you are confused about that is because the second caller is not getting a busy signal. There are several reasons why that is happening:
1. That can happen if your service provider has the option for voice mail, and you did not enable it.
2. Or you specified a large number of rings before going to voice mail.
3. Or you have call-waiting enabled and you are ignoring the beep tones, in addition to reasons 1 and 2 above.
Having said that, I would recommend that you stop using a premises-attached answering machine, and use voice mail instead. That's the only way you can let your callers leave a message while you are talking to someone else. Most phone providers include voice mail service as an additional option these days.