The Sa‘y between As-Safa and Al-Marwah is done in compliance with the practice of Haajar the wife of Prophet Ibraaheem, may Allaah exalt his mention.
My question is, why are men, but not women, required to do Ramal between the two green marks during Sa‘y when they do that in compliance with a woman’s practice?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

It is an act of the Sunnah for men to do Ramal (brisk walking) between the two green marks during Sa‘y between the Safa and Marwah. It is not an obligation to do so.

On the other hand, it is not an act of the Sunnah for women to do Ramal during Sa‘y, even though Haajar did that while hastening between the Safa and Marwah, a practice that was the origin of legislating Sa‘y in general. It is narrated, regarding the Sa‘y of Haajar between As-Safa and Al-Marwah, that, “When she reached the valley, she tucked up her robe and ran in the valley the way a fatigued person does, until she crossed the valley and reached Al-Marwah where she stood and started looking, hoping to see somebody, but she did not see anybody. She repeated that (running between As-Safa and Al-Marwah) seven times.” Ibn ‘Abbaas,   quoted the Prophet, sallallaahu ‘alayhi wa sallam, as saying: “That is why people make Sa‘y between them (i.e. As-Safa and Al-Marwah).” [Al-Bukhari]

Perhaps the rationale behind not legislating Ramal for women is to help them maintain concealment so that no part of their bodies may be disclosed. Explaining the rationale behind Ramal, Ibn Qudaamah said,

In short, doing Ramal in the middle of the valley is a recommended act of the Sunnah, because the Prophet, sallallaahu ‘alayhi wa sallam, and his Companions hastened there. Safiyyah bint Shaybah narrated on the authority of an Umm Walad of Shaybah that she said, ‘I saw the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, hastening between As-Safa and Al-Marwah while saying that the valley should not be crossed except by hastening.’ It is, however, not obligatory to do so, and the one who does not do it is not liable for anything. Ibn ‘Umar and his father, said, ‘That I hasten between As-Safa and Al-Marwah is because I saw the Messenger, sallallaahu ‘alayhi wa sallam, hastening; and that I walk is because I saw the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, walking, and I am an old man.’ Both Hadeeths are narrated by Ibn Maajah and this one is narrated by Abu Daawood. As overlooking Ramal while circumambulating the Ka‘bah is of no consequence, it can be overlooked between As-Safa and Al-Marwah with even greater reason.

Moreover, Ibn Qudaamah said about the rationale behind legislating Ramal for men but not for women, “Ibn Al-Munthir reported the consensus of scholars that women are not required to do Ramal neither around the Ka‘bah nor between the Safa and Marwah. Women are also not required to do Idhtibaa‘. Both Ramal and Idhtibaa‘ are meant to show stamina and women are not supposed to show that. Moreover, women are required to adhere to covering up and concealment, while in performing and Idhtibaa` they become liable to being exposed.”

Allaah Knows best.