The quote you are referring to, from Matthew 8:22, is Jesus' response to a disciple who asked for permission to first bury his father before following Jesus. In this response, Jesus is emphasizing the importance of prioritizing one's commitment to following him over other obligations, even those that might be considered culturally or socially important, like burying one's parent.
The phrase "let the dead bury their dead" is often interpreted as meaning that those who are spiritually dead, or who have not yet committed themselves to following Jesus, will be preoccupied with the affairs of this world and might not understand the importance of prioritizing one's spiritual journey. In this sense, the phrase is a call to action to prioritize one's spiritual life over worldly concerns.
The idea of "pride of life" mentioned in your question is also a biblical concept, found in 1 John 2:16, and refers to the desire for material possessions, social status, and power that are not aligned with God's will. This concept is also related to the idea of worldly concerns and the importance of focusing on spiritual matters.
Overall, the passage from Matthew 8:22 and the concept of "pride of life" emphasize the importance of prioritizing spiritual matters over worldly concerns and the need to follow Jesus and his teachings above all else.