And why did the Jews think Jesus was saying that he had seen Abraham when Jesus just spoke of Abraham seeing his day (and therefore him)?

John 8:56-57 (ESV)

56 Your father Abraham rejoiced that he would see my day. He saw it and was glad.”

57 So the Jews said to him, “You are not yet fifty years old, and have you seen Abraham?”

What is the logical progression here? Is there a translation issue?

I’m looking for how the Jews leaped to questioning that Jesus had seen Abraham rather than questioning how Abraham had seen this day. If you can show how they would be fine with the latter, you still need to solve why they think Jesus is claiming to have seen Abraham (and not the other way around). Or said differently, how did Abraham seeing Jesus’s day also mean or necessitate that Jesus had seen Abraham?

The main question remains how and/or when did Abraham see Jesus’ day, but I want to make sure your answer then informs our understanding of the Jew’s response.