The reason for their disagreement lies in the clash between the relevant reports and the analogy that equates wiping with washing. On this point two contradictory ḥadīths are cited.
The first is the ḥadīth of al-Mughīrah b. Shuʿbah, which states that the Prophet—may Allah bless him and grant him peace—“wiped over the leather sock and its underside.”
The second is the ḥadīth of ʿAlī: “Were religion to rest on opinion alone, the sole of the leather sock would deserve wiping more than its upper side; yet I saw the Messenger of Allah—may Allah bless him and grant him peace—wipe over the upper surface of his two leather socks.”
Whoever seeks to reconcile the two reports treats al-Mughīrah’s narration as recommending the wiping of the sole and ʿAlī’s narration as establishing what is obligatory—a commendable method of harmonisation.
Those who pursue preference (tarjīḥ) choose one report over the other. Whoever gives precedence to al-Mughīrah’s ḥadīth over ʿAlī’s does so on the basis of analogy—that is, likening wiping to washing—whereas whoever prefers ʿAlī’s ḥadīth does so because it runs counter to analogy or because of considerations related to its chain of transmission. In this debate Mālik holds the sounder middle position.
As for the opinion that allows one to wipe only the underside, I know of no proof for it; it follows neither of the two reports nor does it apply the analogy that likens wiping to washing.
Issue Three – The Type of Footwear over Which Wiping Is Allowed
The jurists who permit wiping agree that it is lawful to wipe over a pair of leather socks. They disagreed, however, about wiping over socks (jawrabayn): some allowed it, while others forbade it.
Those who prohibited it include Mālik, al-Shāfiʿī, and Abū Ḥanīfah. Those who permitted it include Abū Yūsuf and Muḥammad—the two foremost disciples of Abū Ḥanīfah—and Sufyān al-Thawrī.
Their divergence springs from two issues: first, the authenticity of the reports that the Prophet—peace and blessings be upon him—wiped over socks and sandals; and second, whether items other than the leather sock may be brought under it by analogy, or whether the ruling is a strictly devotional matter that admits no analogy and may not be extended beyond its specific object. Thus, anyone for whom the ḥadīth was not sound—or never reached him—or who rejected analogy restricted wiping to leather socks. Conversely, whoever deemed the report authentic or accepted analogy allowed wiping over socks as well. This ḥadīth was not recorded by the two Imāms—al-Bukhārī and Muslim—but al-Tirmidhī declared it sound.
Because leather-soled socks (the mujallad socks) fall somewhere between leather socks and ordinary, unsoled socks, two positions are related from Mālik concerning wiping over them: one forbidding it and the other permitting it.