But that is depending on WHAT branch of Jewish faith it is. The liberal branches permit women to be rabbis.
The fact that Jewish women are not permitted to be rabbis has nothing to do with assigning women a "second class" status, BTW. Men and women in Judaism are assigned different roles to fulfill all the tasks which need to be done. Jewish women are considered to be on a higher spiritual level from the get-go. They are exempted from time-related mitzvos, such as making it to the synagogue 3x/day for services, because it is assumed that they have child-rearing duties, for example, which would make that difficult. They also do not have to pray with a minyan (quorum of 10 men). It is considered immodest and it is forbidden to touch men who are not your father, husband or son. Likewise, men are not to touch women who are not their mother, wife or daughter. This would make it very difficult therefore to be a rabbi and be among men all day long. Jewish women are also not encouraged to put themselves forward and be a noticeable part of a mixed group, out of modesty. So you can see where being a rabbi would be outside of Jewish law. This woman does not speak for "The Jews", but rather for herself.