An ostrich egg is classified as an ellipsoid and if we spin it around it's major axis it's classified as a prolate but my fried is arguing that we can not spin that ellipsoid around its minor axis because then "it won't be symmetrical around the axis" and this has confused me.

Does this also mean that we can turn an ellipsoid from prolate to oblate just by changing the axis along which it's spinning?

An ostrich egg is classified as an ellipsoid and if we spin it around it's major axis it's classified as a prolate but my fried is arguing that we can not spin that ellipsoid around its minor axis because then "it won't be symmetrical around the axis" and this has confused me.

Basically I want to know if the same ellipsoid rotated about minor axis that was categorized as oblate, can also be categorized as prolate when we rotate it about the major axis.