The reason, according to the church, is Jesus never chose a woman to be an apostle.
Jennifer O'Malley is one of the most recent women to defy church law and calls herself a woman priest.
"It's a women's rights issue. It's a human rights issue," O'Malley said. "It's time to say that my call is as equal, and as a woman, as a human being, I have to break this law."
The woman priest movement began in 2002 with seven women who were ordained in apostolic succession the same way men priests are. It was performed by a male bishop whose identity is kept secret to prevent his excommunication.
Since then, the movement has grown to nearly 150 women priests worldwide, with California leading the way.
In Long Beach, a couple dozen parishioners recently began meeting monthly. But in San Diego, about 100 gather weekly for mass.
"It's about transforming the whole structure and how it functions," Via said.
As the college of cardinals prepares to elect a new pope, the increasing following of women priests may signal Catholics are losing patience with Rome.
The Archdiocese of Los Angeles declined to comment on the issue, saying it doesn't comment on anything outside the diocese.
But the women's movement hasn't been ignored by the Vatican. In 2010, it labeled the ordination of women a grave crime, the same label it has given to pedophilia, but went a step further by excommunicating any woman who seeks ordination.
There are other Christian denominations that allow the ordination of women, but for these women priests and their followers, Catholicism has formed the spiritual skeleton of who they are and they refuse to abandon it.
While they feel their voices may fall on deaf ears at the Vatican, these women take comfort knowing they can't be silenced.
A few weeks ago, there was a small but significant glimmer of hope for them. One of the voting cardinals, Cardinal Leonardo Sandri of Argentina, gave an interview saying the Roman Catholic Church must open itself up to women in the next pontificate, giving them more leadership positions in the Vatican and beyond.
On Tuesday, not far from the Vatican, symbolic puffs of pink smoke went up in the air as a demonstration by women activists from several countries, including the U.S., who are calling on the cardinals to consider the ordination of women.