The hadith does place a woman, a donkey, and a black dog together in a specific ruling about what passes immediately in front of a person praying. But it does not classify women as animals, nor does it teach that women are impure; the wider evidence and the interpretation of the jurists make that clear.
What the hadith actually says
The strongest form of the objection should be acknowledged: an authentic report says that prayer is "cut off" when one of these passes in front of the worshipper, and Aisha herself objected to the comparison. That is genuinely difficult wording if it is read as a statement about the worth or nature of women.
"The prayer is cut off by a woman, a donkey, and a black dog, when there is nothing before him like the back of a saddle."
Sahih Muslim 510
The wording concerns someone passing directly through the worshipper's immediate prayer space, especially where he has no sutrah - an object placed in front of him as a boundary. It is not saying that women are spiritually equivalent to dogs or donkeys, or that a woman invalidates prayer merely by being visible, nearby, or present in the same room.
Aisha's objection is part of the evidence
Aisha did not quietly accept the idea that a woman was inherently a prayer-invalidating object. She answered that the comparison was unacceptable and testified that the Prophet (PBUH) prayed while she was lying in front of him. Other authentic reports describe people and animals passing in front of the Prophet (PBUH) without him restarting the prayer.
"You have made us equal to dogs and donkeys. I would lie down in front of the Prophet (PBUH) while he was praying, and my legs would be between him and the qiblah."
Reported in the canonical hadith collections, including Sahih al-Bukhari 514 in some numbering systems
These reports show why classical scholars did not treat the first wording as a general statement of female impurity or inferiority. The Prophet's actual practice explains the scope of the report: it addresses a person crossing the direct prayer line, not a woman simply occupying the worshipper's field of vision. The proximity, sudden movement, and interruption of concentration are relevant to the ruling.
How the jurists understood "cut off"
The jurists also differed over whether "cut off" means that the prayer must be repeated or that its concentration and proper form are seriously disturbed. The majority of jurists did not hold that the mere passing of a woman invalidates the prayer in every case. They reconciled the hadith with Aisha's report by restricting it to particular circumstances, such as passing very close in front of the worshipper without a sutrah.
Thus, the hadith establishes a specific prayer etiquette and a disputed legal consequence. It does not establish that women are animals, impure, or lesser human beings. The comparison concerns a technical interruption within prayer, not the dignity, moral status, or humanity of women.