By contrast, al-Shāfiʿī, Aḥmad, the scholars of ḥadīth, Ibn Ḥazm, Shaykh al-Islām Ibn Taymiyyah, and many other critical scholars held it to be pure, supporting their view with numerous proofs, among them:
1- The authenticity of the reports that ʿĀʾishah would scrape the dried semen from the garment of the Messenger of Allah ﷺ with her fingernail. Had it been impure, nothing short of water—like other impurities—would have sufficed.
2- Semen is the very origin and substance of the human being. It is therefore inappropriate for man’s source to be deemed filthy or impure, especially when Allah has honoured and purified him.
3- The Prophet ﷺ never commanded that it be washed or that people take special precautions against it, as he did with urine.
4- They answered the reports that mention washing it by observing that washing does not necessarily indicate impurity; mucus and the like are sometimes washed for cleanliness even though they are not impure. Cleanliness from impurities and repulsive substances is required by the Law, so how could he ﷺ not approve washing it?

Points derived from the ḥadīth
1- Semen is pure, and there is no obligation to wash it from one’s body, clothes, or elsewhere.
2- It is recommended to remove it: if still moist, wash it with water; if dry, scrape it off.

Clarifying that sexual intercourse obligates a ritual bath whether or not ejaculation occurs

Abū Hurayrah, may Allah be pleased with him, reported that the Messenger of Allah ﷺ said: “When he sits between her four limbs and exerts himself, a ritual bath becomes obligatory.” Muslim adds: “even if he does not ejaculate.”

Unfamiliar terms in the ḥadīth
1- “Her four limbs” refers to her arms and legs; it is an indirect way of speaking about intercourse.
2- “Then he exerts her” (with an open jīm and hāʾ) means he strains her to the point of hardship; it is a euphemism for penetration.

Overall meaning
The Prophet ﷺ, in effect, says: When a man sits between a woman’s four limbs—namely, her two arms