That's because he was vested with that specific authority. However, it's revealing that at the Jerusalem Council (Acts 15) it wasn't Peter who rendered the council's decision, but James.
You can even see it here
Pharisees which believed
Acts 15:1 And certain men which came down from Judaea taught the brethren, and said, Except ye be circumcised after the manner of Moses, ye cannot be saved.
Acts 15:2 When therefore Paul and Barnabas had no small dissension and disputation with them,
they determined that Paul and Barnabas, and certain other of them, should go up to Jerusalem unto the apostles and elders about this question.
Acts 15:3 And being brought on their way by the church, they passed through Phenice and Samaria, declaring the conversion of the Gentiles: and they caused great joy unto all the brethren.
Acts 15:4 And when they were come to Jerusalem, they were received of the church, and of the apostles and elders, and they declared all things that God had done with them.
Acts 15:5 But there rose up certain of the sect of the Pharisees which believed, saying, That it was needful to circumcise them, and to command them to keep the law of Moses.
Acts 15:6 And the apostles and elders came together for to consider of this matter.
They concluded
Acts 15:10 Now therefore why tempt ye God, to put a yoke upon the neck of the disciples, which neither our fathers nor we were able to bear?
Acts 15:11 But we believe that through the grace of the Lord Jesus Christ we shall be saved, even as they.
Acts 15:19 Wherefore my sentence is, that we trouble not them, which from among the Gentiles are turned to God:
Acts 15:20 But that we write unto them, that they abstain from pollutions of idols, and from fornication, and from things strangled, and from blood.
Then they wrote
Acts 15:24 Forasmuch as we have heard, that certain which went out from us have troubled you with words, subverting your souls, saying, Ye must be circumcised, and keep the law: to whom we gave no such commandment:
Acts 15:28 For it seemed good to the Holy Ghost, and to us, to lay upon you no greater burden than these necessary things;
Acts 15:29 That ye abstain from meats offered to idols, and from blood, and from things strangled, and from fornication: from which if ye keep yourselves, ye shall do well. Fare ye well.
So really Paul and Barnabas knew what they were talking about, they were at odds with them teaching circumcision and keeping the law of Moses, and so it wasnt "them" who didnt know and had need to go to Jerusalem to ask the other elders and apostles it was because those (who were wrong and at odds with Paul and Barnabas) had determined that they go and ask the other elders and apostles. Paul had said he was unknown by face of them of Judaea Gal 1:22 and thats from where these guys had come down from and started teaching Acts 15:1 These having went out from them there and to whom they gave no such commandment Acts 15:24
The cool thing here is that they knew and trusted the apostles before them enough to be like, Look we dont know you (Paul and Barnabas) not enough for us to take your word on this question we would like you to run this thing by them in Jerusalem, (and it was really unto these guys that they submitted themselves to) and for the gospels sake really (because they were right and the other was wrong and the elders and apostles words should agree with the apostles in this and so they were speaking the same thing
Acts 15:2 When therefore Paul and Barnabas had no small dissension and disputation with them,
they determined that Paul and Barnabas, and certain other of them, should go up to Jerusalem
unto the apostles and elders about this question.
The other cool part of this , is seeing in it how the apostles that come after the former (when the persons were in error or afraid to trust the new guys on the block who come after) as Paul said he was unknown by face of these, and so the latter (even Paul and Barnabs) would submit themselves to those who were in error to cross check themselves to the former in order to dissolve any doubts for the cause of Christ in order to gain them in that way.
Which (to me) should mean the RC has alot of about faces and submitting to do concerning their teachings which always takes you to the traditions Paul mentions but with them more the singular (big T) then you can go there and look in two place in Thessalonians where they can be shown.
I mean it looks like such a small thing but the implications of it are huge when you think of that very small move down there (if set forth as an example to us). That which come after should be willing to submit to what come before it (and this is in the context of apostles as unto apostles (for cross check) and doing so not because someone believes you but to the contrary they dont trust you and so that was route taken, I always thought that was just so awesome really.
Sorry, that was longwinded