On the contrary, we excel at it by pushing things 'down' when we have mastered them.
For instance, driving and talking to a passenger, walking and thinking about something and so on.
We are so good at it that most of the time we don't even notice any more how many things we are doing at the same time.
The only time we are not multitasking is when we are really concentrating on something difficult, usually problem solving or learning a new skill.