We must remember that the Bible, the Word of God is truth (John 17:17b). But there are verses where the Bible reports what was said or done which was untrue (on the part of men and women). This is when the Bible is simply reporting an historic record of events. For example:
Acts 14:11 And when the people saw what Paul had done, they lifted up their voices, saying in the speech of Lycaonia, The gods are come down to us in the likeness of men. 12 And they called Barnabas, Jupiter; and Paul, Mercurius, because he was the chief speaker. 13 Then the priest of Jupiter, which was before their city, brought oxen and garlands unto the gates, and would have done sacrifice with the people.
Paul straightened out this misgiving, but the Bible reported what the people said in error. So just because something is "in the Bible" doesn't mean it is fact or correct. It may simply be historic record.
Note the discrepancies in the Roman soldier's account in Acts 23:26-30 to what previously happened. He made it sound as though he came to Paul's rescue rather than preparing to beat information out of him (contrary to Roman law since it turned out that Paul was a Roman citizen).
The OP has good reason to be confused by the acts of the apostles on this matter.
Acts 1:15 And in those days Peter stood up in the midst of the disciples, and said, (the number of names together were about an hundred and twenty,) 16 Men and brethren, this scripture must needs have been fulfilled, which the Holy Ghost by the mouth of David spake before concerning Judas, which was guide to them that took Jesus. 17 For he was numbered with us, and had obtained part of this ministry. 18 Now this man purchased a field with the reward of iniquity; and falling headlong, he burst asunder in the midst, and all his bowels gushed out. 19 And it was known unto all the dwellers at Jerusalem; insomuch as that field is called in their proper tongue, Aceldama, that is to say, The field of blood. 20 For it is written in the book of Psalms, Let his habitation be desolate, and let no man dwell therein: and his bishoprick let another take. 21 Wherefore of these men which have companied with us all the time that the Lord Jesus went in and out among us, 22 Beginning from the baptism of John, unto that same day that he was taken up from us, must one be ordained to be a witness with us of his resurrection. 23 And they appointed two, Joseph called Barsabas, who was surnamed Justus, and Matthias. 24 And they prayed, and said, Thou, Lord, which knowest the hearts of all men, shew whether of these two thou hast chosen, 25 That he may take part of this ministry and apostleship, from which Judas by transgression fell, that he might go to his own place. 26 And they gave forth their lots; and the lot fell upon Matthias; and he was numbered with the eleven apostles.
Read carefully the text above. I colored the qualifications of an apostle in blue. They left out one very important qualification, being chosen by Jesus. In purple I highlighted who chose whom.
I have tried this same method with the Lord in the past "Lord, which car do you want me to drive, a Porsche or a Lambourgini?" Cast a lot drew a straw did nails paper scissors or whatever to distinguish between the two. This leaves out the third option: NEITHER. Incidentally I ended up with a Ford Escort. <smile>
I underlined above what I believe is a biblically sound insight as to the actual apostleship of Judas and Matthias... that neither were legitimate but only numbered or named among them.
The Bible does not record the calling of every disciple of Christ, but it does mention where one was called but refused to follow (Matthew 19:16-22, Mark 10:18-22, Luke 18:19-24). And there was one who offered to follow Jesus but was shunned:
Matthew 8:19 And a certain scribe came, and said unto him, Master, I will follow thee whithersoever thou goest. 20 And Jesus saith unto him, The foxes have holes, and the birds of the air have nests; but the Son of man hath not where to lay his head. 21 And another of his disciples said unto him, Lord, suffer me first to go and bury my father. 22 But Jesus said unto him, Follow me; and let the dead bury their dead.
Contrast the two men in this this passage. One volunteered and the other was chosen. Yet both were numbered among his disciples (not the reference highlighted in in blue).
The disciples started out as 70 + but then there was a falling away in John 6. And "the twelve" were the core remnant. Jesus' commentary on this was:
John 6:66 From that time many of his disciples went back, and walked no more with him. 67 Then said Jesus unto the twelve, Will ye also go away? 68 Then Simon Peter answered him, Lord, to whom shall we go? thou hast the words of eternal life. 69 And we believe and are sure that thou art that Christ, the Son of the living God. 70 Jesus answered them, Have not I chosen you twelve, and one of you is a devil? 71 He spake of Judas Iscariot the son of Simon: for he it was that should betray him, being one of the twelve.
On the surface it would appear that Jesus did choose each of them. But that's not what he said. He said he chose the group knownas the twelve asnd pointed out that one numbered among them did not belong.
So, it was an incomplete discipleship. Judas never was a legitimate disciple / apostle. There was no position for Peter and the others to fill in Acts 1. This was a job for the Master himself, which he did with the Apostle Paul (the true 12th disciple / Apostle).
And for Paul to have qualified:
Acts 1:21 Wherefore of these men which have companied with us all the time that the Lord Jesus went in and out among us, 22 Beginning from the baptism of John, unto that same day that he was taken up from us, must one be ordained to be a witness with us of his resurrection.
He had to have been one of the 70 or at least among those Jewish leaders who early on in the ministry of Jesus followed along if for no other reason than they were curious. I personally believe he was the rich young ruler and that Jesus' calling for him to follow was irrevocable.
Romans 11:29 for Gods gifts and his call are irrevocable.
The only qualification Saul / Paul lacked was to see the risen Lord. And Jesus appeared to him in his resurrected state on the road to Damascus. When Jesus essentially did to him what he did to Jonah; straightening out his path.