Peter Brandon emphasizes the urgent need for New Testament evangelism in today's world, highlighting the decline of assemblies and the necessity for believers to return to their first love. He stresses the importance of understanding the Gospel, the Trinity's role in salvation, and the reality of a lost eternity, which compels Christians to take their evangelistic responsibilities seriously. Brandon calls for a cleansing of the church and a return to authentic, impactful preaching that reaches out to the lost, urging believers to 'launch out into the deep' and engage with their communities. He illustrates this with the story of Peter's miraculous catch of fish, underscoring the need for depth in evangelism and the importance of humility and brokenness in the face of God's blessings.