You have mentioned that it is not permissible for women to ride horses.

Answer

The laws of the Shariah are the products of Allah's commands which Rasulullah (sallallahu alayhi wasallam) delivered to the Ummah. While Rasulullah (sallallahu alayhi wasallam) handed down the laws, he did not explain the reasons. Thus, Allah Ta'ala ordered two raka'ts for Fajr, four raka'ts for Zuhr and four for Asr, and so on without explaining why Fajr has only two and why Zuhr does not have two, etc.

Our duty is to state the commands of Allah Ta'ala, not the reasons because the reasons were not explained by Rasulullah (sallallahu alayhi wasallam). The issue of 'why' could be directed to all the thousands of masaa-il of the Shariah. Whatever reasons we or any other Ulama present will be the products of personal opinion which may be correct or erroneous. Rasulullah (sallallahu alayhi wasallam) said: "Allah curses women on horseback." In other words the la'nat of Allah Ta'ala descends on women who ride horses. Now why does Allah Ta'ala curse women who ride horses? Rasulullah (sallallahu alayhi wasallam) did not explain the reason. But, we and you and anyone else may think and present reasons. But the reasons will not be divine. They will be our personal understanding. The Muslim need to know only what Allah's law is.

The 'aalimah' is not a mujtahid. She has no right to extract Hadith narrations at random and formulate opinions in conflict with the express command of Allah Ta'ala. When Rasulullah (sallallahu alayhi wasallam) has clearly mentioned that women on horses are accursed, then it is ludicrous and haraam for anyone to present arguments to dismiss what the Nabi (sallallahu alayhi wasallam) said.

Every Hadith has tafseer. It has an explanation and an interpretation. Does the aalimah perhaps know with certitude that riding horses for women is permissible despite Allah's curse on them? She is in grievous error by citing just any narration to satisfy the nafs despite the conflict. It is the function of the Mujtahid to reconcile conflicting narrations or to present the correct interpretation which will not conflict with the Shariah. Every act of every Sahaabi is not the law of the Shariah. Sahaabah had also erred and had misunderstood certain issues. Sahaabah had also acted without being aware of a law which had been announced. A Sahaabi may have done an act before its prohibition, or done it after the prohibition without the law having reached him/her. It was the function of the Mujtahideen to study and investigate the various Hadith narrations and the Qur'aanic aayaat. It was their function to formulate masaa-il. The aalimah is in grievous error by acquitting herself as a mujtahid. May Allah Ta'ala save us from such gross and grave error.