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I.e., he is the spiritual "father" of the whole community (cf. note [8] on verse {6} of this surah), and not of any one person or particular persons - thus, incidentally, refuting the erroneous idea that physical descent from a prophet confers, by itself, any merit on the persons concerned.
I.e., the last of the prophets, just as a seal (khatam) marks the end of a document; apart from this, the term khatam is also synonymous with khitam, the "end" or "conclusion" of a thing: from which it follows that the message revealed through Muhammad - the Qur'an - must be regarded as the culmination and the end of all prophetic revelation (cf. note [66] on the first sentence of the second paragraph of 5:48 , and note [126] on 7:158 ). See also note [102] on 21:107 .
He (ﷺ) is not the father of Zaid (mentioned in 33:37) or any other man. The Prophet (ﷺ) had three biological sons, who all died in childhood.
When a document is sealed, it is complete, and there can be no further addition. The holy Prophet Muhammad closed the long line of Messengers. Allah's teaching is and will always be continuous, but there has been and will be no Prophet after Muhammad. The later ages will want thinkers and reformers, not Prophets. This is not an arbitrary matter. It is a decree full of knowledge and wisdom: "for Allah has full knowledge of all things."