Jesus's brothers had some doubts on why Jesus at that time would not show signs in Judea, especially for one whose name is to be known. At that time, Jesus's brothers did not believe in Jesus, too.
Jesus responds to his brothers' request by saying that "[His] time has not yet come" (7:6). He likely wanted to spend time in other places ministering and doing work (as seen in later chapters) before openly going to Judea to face people who would ultimately kill him at the cross.
Jesus also contrasts himself to his brothers. Jesus pointed out how his brothers have the time to be ready while Jesus would not due to timing. Additionally, because of Jesus pointing out mistakes (as seen in John 2 and 5), Jesus pointed out how the world "cannot hate [Jesus's brothers], but it hates [Jesus]" (7:7). Jesus has been through a lot of areas in the Judean world and encountered a lot people, and it's implied that Jesus's brothers haven't. Thus, the inability for the world to hate Jesus's brothers is based on the current time and due to the world's knowledge. Not to mention that the Greek word for "world" (Strong 2889) can have a meaning of "the multitude or mass" as well as "public".
Even today, sometimes Jesus does not do stuff because of his expert timing. Jesus still does work; he sometimes does not work at the times we expect but works at the unexpected times. Considering that Jesus has a lot of experience (especially in the time department and how he knows hearts), we can be patient, trust in Jesus, and continue to learn from Him during the waiting periods.