Yes the Church's teaching is relevant but it is time for the church to as the saying goes "think outside the box". I would not think of ordination as entitlement but as a call to serve...to provide for Christians the blessings of the sacraments that cannot often reach them without a person to bring these gifts to them.
Dwelling on justice alone does not fit the bill, but full membership as baptized Christians might be the path to grant the ability for the recognition of a possible call to any member.
Our genders are important in the scheme of biology and furtherance of the human species, but we have seen over time, especially recent time, gender does not demand restricted roles in life.
When one reads the Eucharistic prayers it clearly shows that a person leading the Community is repeating the words and actions of Jesus in offering the bread and wine as He did to those gathered. The presider does not ever identify themselves as Christ but does what Jesus said to do.
Peace...Joan