Why can't you just take my non-emergency call on 9-1-1 when we are both on the line already?

It is highly important to use 9-1-1 only for emergency situations. When people call 9-1-1 for non-emergency situations the 9-1-1 phone line is then tied up and unavailable for people with emergency situations. The mother with the choking child may not be able to reach emergency services, because the line is busy.