In addition to upcoming persecutions, Jesus also told the disciples that he would later be away from the disciples. In one sense, Jesus would die on a cross by himself, but even after the resurrection, Jesus would later ascend to heaven and would no longer be there in person (as seen in Acts 1).
When the disciples learned that they would not be with Jesus in person, they felt sorrow. However, Jesus told the disciples that the going away would actually be a good thing because Jesus not only goes with the Father but also delivers the Holy Spirit (16:7). Previously, in John 14, Jesus talked about how the Holy Spirit teaches them, helps them remember Jesus's teachings, and is basically the ultimate Helper while residing with them anytime, anywhere. So while the disciples may not always get to be with Jesus in person, they would later always get the companionship of the Holy Spirit.
By the way, regarding Jesus's comment on how the Helper would not come if Jesus did not go away, it's likely that the Holy Spirit chose to enter after Jesus's ascension to demonstrate that we don't need a physical location to experience Jesus. Rather than over-relying on physical presence, we can know that God is spiritually present and with us (via Holy Spirit) anytime, anywhere.