Why does Paul pay special attention to the sexually immoral in 1 Corinthians 5:9-11?

If we take a look at the surrounding context, we see that Paul is dealing with a case of sexual immorality within the church:

1 Corinthians 5:1-2 (NASB)
¹ It is actually reported that there is immorality among you, and immorality of such a kind as does not exist even among the Gentiles, that someone has his father’s wife. ² You have become arrogant and have not mourned instead, so that the one who had done this deed would be removed from your midst.

So he is specifically dealing with sexual immorality in the context, and basically tacks on "and for that matter, not greedy, swindlers, or idolaters either". It is evident that in the passage you cite (v 9-11), he is still operating in the context set up in v 1-2, because he goes on in verse 13 to say:

1 Corinthians 5:13 (NASB)
¹³ But those who are outside, God judges. REMOVE THE WICKED MAN FROM AMONG YOURSELVES.

The Apostle John actually commands believers to not associate with those professing to be believers who deny that Jesus came in the flesh.

For many deceivers have gone out into the world, those who do not confess the coming of Jesus Christ in the flesh. Such a one is the deceiver and the antichrist. 8 Watch yourselves, so that you may not lose what we have worked for, but may win a full reward. 9 Everyone who goes on ahead and does not abide in the teaching of Christ, does not have God. Whoever abides in the teaching has both the Father and the Son. 10 If anyone comes to you and does not bring this teaching, do not receive him into your house or give him any greeting, 11 for whoever greets him takes part in his wicked works. 2 John 1:7-11 ESV

Additionally, Jesus Himself taught that there times when believers should disassociate from others who claimed to be believers:

“If your brother sins against you, go and tell him his fault, between you and him alone. If he listens to you, you have gained your brother. 16 But if he does not listen, take one or two others along with you, that every charge may be established by the evidence of two or three witnesses. 17 If he refuses to listen to them, tell it to the church. And if he refuses to listen even to the church, let him be to you as a Gentile and a tax collector." Matthew 18:15-17 ESV

For a Jew at that time, there was strict rules about associating with Gentiles (those who did not worship the one true God).

Of course, no one--Christian and non-Christian and even atheist alike--should ever associate with tax collectors. That's a universal moral absolute.

Paul's instructions are directed at a specific case that was occurring in the Corinthian church, so he didn't mention those who deny that Jesus came in the flesh or because that wasn't an issue in the Corinthian church at the time--really bad sexual immorality was.

So, sexual immorality is not singled out in the body of Scripture for disassociation--it's just mentioned because it was occurring in this specific instance.

Just a quick note to add to a helpful question and answers.

Many overlook that Paul's emphasis on sexual immorality flows from the Jerusalem Council's ruling in Acts 15, where they explicitly instructed him to address certain topics to the churches he planted. Sexual immorality and avoiding practices that caused division--those were the two topics they told him to address.

Thus, you get 1 Corinithians. Thus you get 1 Thes 4. And you get, in all the lists of activities that unrepented, will pave the way to hell--sexual immorality (conjoined with idolatry) leads the way, every time.

So I'm not sure it's always best to read that in every town, or throughout the culture, sexual immorality was necessarily "rampant" and that this existent problem was his motive for writing on the topic.

The motive can be traced to the problems and solutions that Acts 15 addresses--that sexual immorality and culture-based ceremonial offenses (partial list given in Acts 15 full list given in Lev 18-20) would tear about the church, tear apart Paul's ministry.

I'm not sure Paul is singling out the sexually immoral. The only place they are mentioned exclusively is when he talks about his previous writing. Everywhere else he says " immoral, or the greedy and swindlers, or idolaters...". I would take that as a deliberately inclusive list - i.e. he is making a long list to make it clear that he's talking about all kinds of morality. A possible interpretation is that he wrote previously about sexual immorality for some reason, and now he's is having to correct a few misinterpretations, one being that sexually immorality is a special kind of immorality.