Impurities Leaving the Body and Wuḍūʾ

The disagreement

Scholars agreed on the nullification of ablution (wudu) by what exits from the two pathways such as urine, feces, wind, madhiy, and wadiy.
They disagreed if impurity exits from [other parts of] the body, does it nullify ablution?

The opinions

Ablution is nullified by every impurity (najis) exiting from any part of the body, such as blood, nosebleeds, and vomiting:
Held by: Abū Ḥanīfah / Aḥmad / al-Thawrī.
Ablution is nullified by every exit from the two pathways regardless of how it exits—whether due to health or sickness, such as blood, stones, worms, and phlegm:
Held by: al-Shāfiʿī
Ablution is nullified by everything that exits from the two pathways (al-sabilayn) in a habitual manner, like urine and feces, provided its exit is in a healthy state:
Held by: Mālik.

Reason for the disagreement

The possibilities found in the Muslim consensus regarding the nullification of ablution by what exits from the two pathways—such as feces, urine, wind, madhiy, and wadiy—due to the apparent text of the Book:

﴿أَوْ جَاءَ أَحَدٌ مِّنكُم مِّنَ الْغَائِطِ﴾

"or one of you comes from the place of relieving himself" [An-Nisāʾ: 43].

And due to the apparent meaning of the prophetic reports (zahir al-athar) regarding that, such as the ḥadīth: «لَا يَقْبَلُ اللَّهُ صَلَاةَ مَنْ أَحْدَثَ حَتَّى يَتَوَضَّأَ»

"Allah does not accept the prayer of one who passes ritual impurity until he performs ablution." [Agreed upon / Muttafaq 'alayhi].

Evidence

For the first opinion:
What matters is the exiting impurity itself; because the ruling of nullifying purity is tied to it. Therefore, the impurities exiting from the body affect purity. (Meaning, the agreed-upon events of ritual impurity are specific instances intended to convey a general rule).
The ḥadīth of Thawbān ﷺ: "That the Messenger of Allah ﷺ vomited, so he broke his fast and performed ablution." (Reported by:/-Ahmad, al-Tirmidhī; and al-Albānī authenticated it).
It is authentically reported from ʿUmar and Ibn ʿUmar رضي الله عنهما that they both performed ablution due to nosebleeds [Reported by: al-Muwaṭṭaʾ ].
His ﷺ command to the woman experiencing prolonged non-menstrual bleeding (al-mustahadah) to perform ablution for every prayer, and his saying: «إِنَّمَا ذَلِكَ عِرْقٌ وَلَيْسَ بِحَيْضَةٍ» "That is only a vein and is not menstruation." (Reported by://-Ahmad, Abū Dāwūd, Ibn Mājah; and al-Albānī authenticated it). This indicates the obligation of ablution for every blood flowing from the body.
For the second opinion:
What matters is the exit pathway; because the ruling of nullifying purity is tied to them. Thus, they are the events of ritual impurity agreed upon.

(الخاص الذي أريد به العام) (Meaning, they are specific instances intended to convey a specific rule). Therefore, the purpose of the rule is the pathway due to their agreement on the obligation of ablution due to wind exiting from below, and the absence of its obligation if it exits from above. Both are one thing [wind], but they differ in the pathway of exit.

His ﷺ command to the woman experiencing prolonged non-menstrual bleeding (al-mustahadah) to perform ablution for every prayer, as prolonged bleeding is a sickness.
For the third opinion:
What matters is the exit pathway and the description of the exit; because the ruling of nullifying purity is tied to them.

(الخاص الذي أريد به الخاص) (Meaning, the agreed-upon events of ritual impurity are specific instances intended to convey a specific rule). Thus, it does not apply to other than that.

Because ʿUmar ﷺ prayed while his wound was bleeding profusely and he did not cut off his prayer (Reported by://-al-Muwaa Abdal-Razzāq; and al-Albānī authenticated it).

References

Bidāyat al-Mujtahid wa Nihāyat al-Muqtaṣid (1/68), Tabyin al-Haqa'iq (1/45), al-Bahr al-Ra'iq (1/58), al-Tafri' (1/196), al-Maʿūnah (1/45), Nihayat al-Matlab (1/119), al-Bayan (1/170), al-Sharh al-Kabir (2/12), al-Mughni (1/233), Sharh Ibn Zāḥim (1/204).