There's a certain stubbornness in the Israelites' response. 'No! But...' — this phrase reveals a mindset that's already decided and unwilling to listen.
The phrase 'No! But there shall be a king over us' is a powerful declaration of willful independence. They aren't open to discussion or correction; their minds are made up. Samuel, representing God’s authority, has just laid out the negative consequences of having a king, essentially warning them against this path. Their response is a forceful dismissal of his counsel and a doubling down on their decision. It reveals a desire for an external, visible leader – a king – as a substitute for the internal, spiritual reality of God’s direct kingship over them.