This is the main problem: People like Avi Weiss and YCT believe that the primary point of the Torah is chesed, which is a very valid belief.
If that is the case, then it raises many difficulties in some of our practices, which are legitimate kashyas, just like any other kasha in any sugya.
For example, they grapple with how one can be commanded to kill a child of certain nations. This is a very serious question. It is compounded by the fact that simple answers like they will grow up to be wicked, is also a justification for the Nazis killing our children.
So it is very convenient for the Chareidi world to just smugly say that our religion says so, end of story. Because that raises questions as to how we look on in horror when an Islamic terrorist kills one of our children. He believes just as strongly that his religion is the only true one, and has commanded him to kill Jewish children R”L (case in point, the Fogel murders).
So while one may disagree with Avi Weiss’s answers or his approach to these difficult questions, but I highly doubt anybody from the Chareidi world has any answers at all. It is convenient to just ignore things that one doesn’t want to face, and go around smugly patting oneself on the back for being a very religious person.
Another issue the people of Avi Weiss’s camp raise is if a woman can be a brain surgeon these days, why can’t she study gemara? Remember that Sarah Schenirer also met with opposition when she founded the Bais Yaakov movement, because it was against the mesora. However, because girls were then required to go to school for secular subjects, it was reasoned that she must have a Jewish education, as well. Should girls just be taught pirkei avos these days, when they go to college and medical school and learn sophisticated subjects of all other kinds?
The questions are not easy, but ignoring them is.