The obvious reason the Prophet (sawa) had the Epithet or nickname of Abul-Qasim was that he had a son by the name of Qasim (as). However, is there a deeper meaning?..
Muhammad ibn Ibrahim ibn Ishaq al-Taliqani – may God be pleased with him – narrated that Ahmad ibn Muhammad ibn Sa’eed al-Kufi quoted on the authority of Ali ibn Al-Hassan ibn Ali ibn Fadhdhal, on the authority of his father:
I asked Abal Hassan Al-Reza (as), “Why was the Prophet’s (sawa) nickname Abul-Qasim?” Al-Reza (as) said, “It was because he had a son named Qasim. That was why his nickname was Abul Qasim.”
I asked him, “O son of God’s Prophet (sawa)! Do you consider me worthy of more explanation?” Al-Reza (as) said, “Yes. Don’t you know that God’s Prophet (sawa) said?, “Ali and I are the fathers of this nation.” I said, “Yes, I do.” Al-Reza (as) said, “Don’t you know that God’s Prophet (sawa) is the father of all the nation, and Ali is one of the members of this nation?” I said, “Yes.” Al-Reza (as) said, “Don’t you know that Ali (as) is the ‘Qasim or the one who divides up Paradise and Hell?” I replied, “Yes.” Al-Reza (as) said, “Then that is why the Prophet (sawa) is called Abul-Qasim – as he is the father of the one who divides up Paradise and Hell.”
I asked, “What does this mean?” Al-Reza (as) replied, “The kindness of the Prophet (as) for his nation is like that of a father for his children. The noblest member of his nation is Ali (as). And after him the kindness of Ali (as) for them is like the kindness of the Prophet (s), since he is the Prophet’s (s) Trustee, Successor and the Divine Leader after the Prophet (sawa). That is why the Prophet (sawa) said, “Ali and I are the two fathers of this nation.” God’s Prophet (sawa) climbed up the pulpit and said, “Whoever leaves behind a debt or a wife, I must repay his debt and pay for the living expenses of his wife. Whoever leaves behind some property, that property will belong to his inheritors.” That is why the Prophet (sawa) was superior to their fathers, mothers and even themselves. The same thing held true for the Commander of the Faithful (as) after God’s Prophet (sawa).”
Source: `Uyoun Akhbar Al-Ridha, Sh. Al-Sadooq, Volume 2, Pages 91-92 (See Image)
The Prophet (sawa), when a Jew asked him about the reason for him being called Muhammad, Ahmad, Abu al-Qasim, Bashir, Nadhir, and Da`ai – he replied, ‘As for Muhammad, I am praised [mahmud] in this earth, and Ahmad is that I am praised in the Heaven. As for Abu al-Qasim, Allah will divide the Day of Resurrection into two parts; the part (qisma) of Hell, and those who disbelieve in me from among the first ones to the last ones will be in the Hellfire; and the part of Heaven, and whoever believes in me from among the first ones to the last ones, and has acknowledged my prophethood will be in Heaven. Al-Da`ai [the caller] is that I call people to the religion of my Lord Almighty. Al-Nadhir [the warner] is that I warn people who disobey me about the Hellfire. Al-Bashir [bringer of good news] is that I bring the good news of Heaven to those who obey me.’
Source: Ma`ani al-Akhbaar, Sh. al-Sadooq (rh), Page 51-52, Hadith #2 (See Image below)