The notion of ambidexterity is valid, and some people do show equal proficiency in various manual skills with both hands.
However, hand-use preferences are on a continuum, and a mere three categories of left-handed, right-handed and ambidextrous are artificial divisions.
One researcher calls ambidextrous people ambilateral, and further divides them into the ambidextral, those with both hands as skilled as a right-hander’s right hand, and the ambisinistral, those with both hands as skilled as a right-hander’s left hand.
It is common for an individual to find some skills to be easier for one hand while others fall more easily into the other hand’s grasp.
The explanation is that two sets of factors are involved in which hand acquires which skills, the child’s own capacities and hand-use preferences, which even young infants have established, and the skills modeled on the way other people do things, even contrary to their own preferences.
For example, if a left-handed child is being taught to pitch a ball, most adult pitchers are right-handed, and the way they demonstrate the skill will be affected by these preferences, so the child must adjust in order to acquire the way they use the skill.
Left-handers as a group are much less strongly left-handed than right-handers are right-handed.
Researchers have discovered that it is much easier to learn a skill like knitting if the pupil’s hand preference matches that of the teacher.
A left-handed guitar student who has to see demonstrations by a right-handed teacher is at a disadvantage.
Paul McCartney of the Beatles is a classic case.
A left-hander, he had difficulty learning to play until he restrung his guitar.