Jesus' brothers urge him to leave Galilee and go to Judea so his works can be seen publicly. Jesus initially refuses their timetable, then later goes to the feast 'not openly, but as it were in secret.'
The exchange assumes that Jerusalem during Tabernacles was a major public stage.
Tabernacles belonged to Israel's pilgrimage festival tradition, bringing worshipers toward Jerusalem and the Temple. Travel from Galilee to Judea placed Jesus among large movements of pilgrims and exposed him to the Jerusalem authorities already hostile toward him in John's narrative.
John's contrast between public display and Jesus' less conspicuous arrival concerns timing and manner, not a contradiction about whether he attends the feast at all.
The pilgrimage setting explains his brothers' logic: if Jesus wants public recognition, a major Jerusalem festival appears to be the obvious place to seek it.
John instead emphasizes that Jesus acts according to the Father's timing. He does go to Jerusalem, but not as a performer controlled by family pressure or popular expectations.