The argument has force only if Muslims reject Paul simply because he came later and never met Jesus. That is not the real Muslim criterion: the issue is not mere distance in time, but whether a teaching is confirmed by God's revelation.
Why the objection sounds strong
The critic's best point is this: Paul is earlier than Prophet Muhammad (PBUH), closer to the first Christian generation, and his letters are among the earliest Christian writings we possess. If Muslims say, "Paul did not meet Jesus, so we reject him," then it seems inconsistent to accept Prophet Muhammad (PBUH), who came about six centuries later and denied central Christian doctrines: crucifixion, resurrection as saving event, and divine sonship.
Stated that way, the objection exposes a weak popular argument sometimes made by Muslims. "Paul never met Jesus" by itself is not enough. Many reliable people transmit truth from those they did not personally meet. A later messenger could be true, and an earlier teacher could be mistaken. Time alone does not settle the matter.
The Muslim criterion is revelation, not proximity alone
Muslims reject Paul's theology because it conflicts with what the Quran presents as the restored message of Jesus: worship God alone, obey His commandments, and do not make Jesus divine. Prophet Muhammad (PBUH) is not accepted as a historian making a late guess about Jesus; he is accepted as a prophet receiving revelation from the same God who sent Jesus.
"And when Allah will say, 'O Jesus, son of Mary, did you say to the people, "Take me and my mother as two gods besides Allah"?' He will say, 'Glory be to You! It was not for me to say what I had no right to say.'"
Quran 5:116
"They did not kill him, nor did they crucify him, but it was made to appear so to them... Rather, Allah raised him to Himself."
Quran 4:157-158
So the Muslim position is not: "Paul is late, therefore false; Muhammad is later, yet true." It is: "God sent prophets with one religion of worshipping Him alone; later communities differed; the final revelation judges between those differences."
"I am the closest of all people to Jesus son of Mary in this world and the Hereafter. The prophets are paternal brothers; their mothers are different, but their religion is one."
Sahih al-Bukhari; Sahih Muslim
What about the disciples?
The objection assumes that Paul's doctrines are simply "what Jesus' own disciples preached." Muslims do not grant that assumption. The Quran praises the true disciples of Jesus as believers and helpers of God, not as preachers of Jesus' divinity.
"The disciples said, 'We are the helpers of Allah. We believe in Allah, and bear witness that we are Muslims.'"
Quran 3:52
Historically, too, the matter is not as simple as "the disciples said X." We do not possess signed theological treatises from all twelve disciples laying out Nicene Christology. The earliest Christian writings are Paul's letters, and the Gospels are later than Paul's earliest letters. Christians may still argue that their tradition faithfully preserves apostolic preaching, but that is a theological claim, not a neutral historical fact that automatically defeats Islam.
What the argument does and does not prove
The argument does prove that Muslims should not use a shallow slogan: "Paul never met Jesus, so Paul is false." That is not enough.
But it does not disqualify Prophet Muhammad (PBUH), because Islam is making a different kind of claim: that God corrected earlier religious disputes through final revelation. If the Quran is from God, then its testimony outweighs later or earlier human disagreement. If someone rejects the Quran from the start, then of course he will not accept its correction of Christian doctrine - but that is where the real debate lies.
So the honest question is not, "Who came closer in time?" It is, "Has God spoken, and which revelation bears the marks of His speech?" That is the ground on which Islam asks to be judged.