A private meeting is more conducive to frank and open discussion than one that is in public in front of a large number of people.1 It is very likely that Paul was aware of the Judaizer pressure groups in Jerusalem and that he did not want to give them a chance to influence discussions unduly.
2 I went up because of a revelation and set before them (though privately before those who seemed influential) the gospel that I proclaim among the Gentiles, in order to make sure I was not running or had not run in vain.