Abu Bakr al-Humaydi (may Allah have mercy on him) said: I heard Yahya bin Sa'id al-Qattan (may Allah have mercy on him) ask Sufyan bin Uyaynah (may Allah have mercy on him) about this hadith, namely: "We performed tayammum with the Messenger of Allah (peace and blessings be upon him) up to the shoulders." Sufyan (may Allah have mercy on him) said: I was present with Isma'il bin Umayyah (may Allah have mercy on him) when he came to al-Zuhri (may Allah have mercy on him) and said: O Abu Bakr! People object to two of your hadiths! He asked: Which are they? He said: "They performed tayammum up to the shoulders."
Al-Zuhri (may Allah have mercy on him) said: It is narrated from Ammar (may Allah be pleased with him): "We performed tayammum with the Prophet (peace and blessings be upon him) up to the shoulders." Isma'il (may Allah have mercy on him) said: The hadith of Ubaydullah mentions touching the armpits.
It is narrated from Ubaydullah that Sayyiduna Umar (may Allah be pleased with him) ordered a man to perform ablution because he had touched his armpits.
The hadith about touching the armpit is mursal: Ubaydullah bin Abdullah bin Utbah did not meet Umar bin al-Khattab, and al-Zuhri disowned it after having narrated it.
Sometimes the order to wash the hands is given for the sake of cleanliness. And Allah knows best.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 655
Sayyiduna Ibn Umar (may Allah be pleased with them both) narrated: When a person performs ablution and then touches his armpits, he should repeat the ablution.
(b) It is narrated from Ibn Abbas (may Allah be pleased with them both) that he is not required to repeat it.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 656
Yahya al-Bakka' said: I saw Sayyiduna Ibn Umar (may Allah be pleased with them both) put his hand into his armpits while in prayer, and still he continued his prayer.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 657
(a) It is narrated from Nafi' (may Allah have mercy on him) that Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) would perform ablution in hot weather and pass his hands over his armpits, and that did not break his ablution.
(b) Yahya bin Sa'id al-Ansari, Yazid bin Abi Habib, al-Layth bin Sa'd and Malik bin Anas (may Allah have mercy on them) said: There is no ablution for touching the armpits; Ibn Wahb (may Allah have mercy on him) reported this.
(c) The Shaykh (may Allah have mercy on him) said: This is the view of Imam al-Hasan al-Basri (may Allah have mercy on him) and al-Harith al-Ukli (may Allah have mercy on him), of the Successors (Tabi'in). This is also the position of Imam al-Shafi'i (may Allah have mercy on him).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 658