The answer to the titled question of “Why Paul” is; because it pleased God to use Paul and Paul alone as the human agent through whom He would proclaim and reveal the present-day administration of “the grace of God.”

This grace is given to me [Paul] (who am less than the least of all saints) to preach the gospel of the unsearchable riches of Christ among the nations [Gentiles v1], and to bring to light what is the fellowship (dispensation some versions) of the mystery which from eternity has been hidden in God, who created all things by Jesus Christ; Eph 3:8-9

We Gentiles have a relationship to Paul as “the Apostle to the Gentiles” (Rom. 11:13) that we do not have to any other apostles. It is essential that we prayerfully seek to discover this unique relationship and Paul’s unique message for ALL men today.

First, we need to remove some misunderstandings among many Christians.

Foremost, Paul was not, and could not be, one of Jesus’ Twelve Apostles. The passage Acts 1:15-26 narrates the choosing of Matthias to replace Judas, and this was not conducted by ignorant men, but by those who had been instructed for 40 days by the risen victorious Saviour. He had also "opened" their understanding of the Scriptures, and so their actions were in accordance with the Scriptures;

And He [Jesus] said to them [the twelve], These are the words which I spoke to you while I was still with you, that all things must be fulfilled which were written in the Law of Moses and in the Prophets and in the Psalms about Me. And He opened their mind to understand the Scriptures. Luk 24:44-45

... He also presented Himself living after His suffering by many infallible proofs, being seen by them through forty days, and speaking of the things pertaining to the kingdom of God [to come on earth as was promised]. Act 1:3

The ordination of Matthias took place approximately seven years before Paul's "conversion," but even this is not the complete answer to Paul's unsuitability. Paul was not divinely qualified to be one of the Twelve as seen by this verse

Wherefore of these men [the twelve] which have accompanied with us all the time that the Lord Jesus went in and out among us, beginning from the baptism of John unto the same day that He [Jesus] was taken up [ascended to heaven] from us, must (of necessity) one Be Ordained To Be A Witness With Us Of His Resurrection.
Acts 1:21

Paul was not among “the twelve” from the time of Jesus’ water baptism. Nor was Paul there when Jesus ascended to heaven. Paul’s later calling came after the initiation of the “fall of Israel” with Israel stoning Stephen to death in Acts 7:58. Israel had already killed all the prophets Gd sent them, then they killed the prince of Peace, Jesus. In killing Stephen they killed a man “full of the Holy Spirit.” With Israel’s rejection of the Triune God, God turned to the Gentiles. With that, soon after this momentous event, the Lord Jesus from heaven called, saved, and commissioned Saul of Tarsus (Paul) as recorded in Acts 9, to be his minister to ALL men alike.

Compare the first instruction or commission Jesus gave to “these twelve” of Israel with that of the of the calling given to Saul Paulus (Paul) the day he was commissioned. These verses defined exactly Who They Were To Go To as their First Objective.

The Twelve Apostles:

⁵ These twelve Jesus sent forth, and commanded them, saying, Go NOT into the way of the Gentiles, and into any city of the Samaritans enter ye not: ⁶ But go rather to the lost sheep of the house of Israel. Matthew 10:5-6 (KJV)

The Apostle Paul:
¹⁵ But the Lord said unto him [Ananias], Go thy way: for he [Paul] is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel: ¹⁶ For I will shew him [Paul] how great things he must suffer for my name's sake. Acts 9:15-16 (KJV)

Do you see the stark contrast in the above verses.

• The twelve Apostles were sent only to the lost sheep of the house of Israel.
• The Apostle Paul was “a chosen vessel unto me [the Lord], to bear my name before the Gentiles, and kings, and the children of Israel:”

Much later, after the 35-year Acts period ends, Paul says his life was the “first [the prototype]” to be “a Pattern” for those who would believe unto life everlasting after the Acts Period Ended, during today’s “dispensation of the grace of God.”

¹⁵ This is a faithful saying, and worthy of all acceptation, that Christ Jesus came into the world to save sinners; of whom I [Paul] am chief. ¹⁶ Howbeit for this cause I [Paul] obtained mercy, that in me FIRST [Grk. protos, the prototype] Jesus Christ might shew forth all longsuffering [His patience], for a PATTERN to them which should hereafter believe on him to life everlasting. 1 Timothy 1:15-16 (KJV)