John 15 is a continuation of Jesus’s “I am” statements from John chapter 14. Jesus is making a connection between the one true God and himself. “The earlier sayings had focused on Jesus as the life-giver and had included an invitation to come to him and to believe in him (6:35; 8:12; 10:9; 11:25–26; 14:6). Now, however, Jesus is speaking to those who have already come to him, and so his charge is that they remain in him (cf. Michaels 1989:271). The earlier theme of life is now developed in terms of intimate union with Jesus, a sharing in his own life. Thus, this is a fitting conclusion to the ‘I am’ sayings. … Jesus stresses the impossibility of producing this fruit apart from him (vv. 4–5). People are able to produce much without God, including converts, good deeds and even prophesies, exorcisms and miracles (cf. Mt 7:22–23; Ridderbos 1997:517). But the divine life such as we see in Jesus is dependent on God’s own character, power and guidance at work in the life of the disciple. Jesus did not will nor speak nor act from himself; neither is the branch capable of bearing fruit ‘from itself’ (v. 4 …). Hence Jesus’ command to remain in me (v. 4)” (Rodney A. Whitacre, John, The IVP New Testament Commentaries [Downers Grove, IL: IVP, 1999], Logos 9).
A branch cannot live apart from the trunk or vine of a plant. In horticulture, nutrients and water flow from the main stem or trunk of the plant to the outer branches or stems. From there the nutrients create fruit or leaves to cover the plant. A branch cannot grow fruit or leaves if it is not connected to the center of the plant. “Over the growing season, the ‘mother’ plant receives sunlight, water, and nutrients from the soil to keep growing, helping the immature fruit to continue growing larger” (“Wonder of the Day #1839: How Do Plants Make Fruits and Vegetables?” Wonderopolis, https://www.wonderopolis.org/wonder/how-do-plants-make-fruits-and-vegetables).