Jesus asked the disciples if they want to leave Jesus (just like other people), but Peter talks about how Jesus's words are reliable.
However, Jesus talks about how he chose the original twelve and he knew that one of them "was a devil" (6:70). He was referring to Judas Iscariot, and as we'll see later, Judas was the one to betray Jesus (6:71). The word for "devil" (Strong 1228) can be interpreted as "backbiter" or "slanderer", which is also an accurate description of what Judas would be later on. He proclaimed such statements because he knew the hearts and attitudes of the disciples -- including Judas. Even though Judas may stick with Jesus in person (unlike other people), his heart isn't necessarily with Jesus.
Even today, Jesus knows our hearts. If we're honest, our motives can be problematic to others. Jesus knows that, and as we saw in John 3, he wants to renew us because of our problematic motives (and even instincts).