Tongues were sign for unbelievers, not for believers.
I think one must make a distinction between the
gift of tongues and the
manifestation of tongues. You'll agree with me that not every believer has the gift of tongues, to each are given specific gifts (some more than others, depending upon the Lord's will). So, when a believer has been baptized in the Holy Spirit and starts speaking in tongues (as evidenced throughout scripture), you would agree that not every single one of these people received the gift of tongues, right? Just a manifestation as an outward representation (and more) of what just took place.
So then the gift of tongues differs in purpose from the manifestation of them. Here is one obvious difference between the gift of tongues and the manifestation of them. At Pentecost you'll notice that tongues were
not translated, no interpretation was necessary. Yet, if you read 1 Corinthians 14 it speaks of the
gift of tongues needing to be interpreted with the
gift of interpretation. These are both spiritual gifts.
Pentecost, indeed, had the manifestation of tongues that were a sign to unbelievers. Keep this in mind, however, that just because tongues are a sign to unbelievers it doesn't mean that the gift of tongues are not a gift for the edification of the Body of Christ. That is where there is a leap in logic. A sign to an unbeliever doesn't automatically equate to the gift being unedifying to the Body of Christ. So to insinuate that the apostle Paul was suggesting that tongues are not for believers is false. They are not a
sign to believers, but they are still
edifying to believers (as is the purpose of all the gifts).