It has not been proven that women are better at multitasking
It has not been proven that women are always better at multitasking than men. This is because 'successfully multitasking' is heavily influenced by other factors.
Same or different brain processes?
One such factor is whether two tasks utilize the same or different brain processes. This makes singing, (an auditory process), easy to combine with riding a bicycle (a motor process), as both tasks utilize different brain processes. On the other hand, singing is hard to combine with listening to the news because many of the same brain processes are involved in these tasks. This goes for men and women.
A second factor is experience. If you are experienced at certain tasks, they seem to go 'automatically'. As you think less while performing these tasks, your brain has more remaining capacity for other tasks. This is why an experienced chef can prepare multiple dishes at the same time while an entry-level cook has to concentrate while baking an egg.
As such, the ability to multitask while cooking does not depend on whether you are a man or a woman, but mostly on how often you cook.
Chris Janssen, Assistent Professor Experimental Psychology