1. The Lord told His disciples to wait until the coming of the Holy Spirit (Luke 24:49). Wait is not the same as "don't do anything at all." Following the Scriptures was not a violation of waiting in Jerusalem. And in fact, they were in Jerusalem when the selection occurred.
2. The Lord did not instruct His disciples to replace Judas. This is an assumption based on silence. By silence we can assume that the Lord did not instruct His disciples to replace Judas and Peter just dreamed up the idea, or that the Lord brought it to His mind in the post-resurrection instructions, through the Spirit, and/or through the Word. The facts that Luke records should outweigh our assumptions.
3. The disciples/apostles had never chosen other apostles before this. The original twelve disciples were chosen by Jesus Himself. In itself this is an irrelevant objection. There was never a reason to choose other apostles before this time.
4. The selection of Matthias was held before Pentecost, before the Holy Spirit had come upon them. The Holy Spirit had already been breathed on these men (John 20:22).
5. The selection of Matthias occurred in what was still technically Old Testament time. The New Testament time begins with the announcement of Jesus, not the day of Pentecost. See Mark 1:1, et al.
6. The selection of Matthias was completed by casting lots. This practice was an Old Testament practice for discovering God’s will (Lev. 16:8-10; Prov. 16:33). This was also a New Testament practice for discovering God’s will – at least this once – as evidenced in Acts 1! One cannot simply exclude something because he doesn’t like it.
7. Matthias is never mentioned again in the Scriptures. But he is! Though not by name. He is mentioned in Acts 2:14 and Acts 6:2, for example. All the apostles are mentioned numerous times as "the apostles" but only are few of them are mentioned by name in the book of Acts or the rest of the New Testament. Such an indictment against Matthias' apostleship would indict the office of the majority of the twelve apostles.
8. Luke mentions "the eleven" instead "the twelve" in Acts 2:14. Not until Paul was chosen were there again 12 apostles. This is wrong on several counts. First, in Acts 2:14, Peter plus eleven more apostles makes a total of twelve. Second, the twelve are mentioned in Acts 6:2, before Paul was called on the road to Damascus. In fact the apostles are mentioned about 20 times between Acts 1 and Acts 9, with never the least hint that Matthias is not an apostle. Third, James (Gal. 1:19) and Barnabas (Acts 14:4,14), who are also called apostles, were chronologically prior to Paul.
9. Paul was the twelfth apostle and therefore Matthias could not be. Paul was hand picked by Christ to be an apostle. The first statement is circular reasoning, pure and simple, merely assuming what is to be proven. The second is a true statement that does not address the first. Chronologically Paul was not the “twelfth” apostle – not even the thirteenth or fourteenth. James and Barnabas were chronologically prior to Paul.