This could have been an opportunity for both of you to understand each other's perspective. That's why you asked their thoughts on the matter right? It's a shame you let that pass you by.
And if you think they'y aren't ending, you need to go look at the numbers and then look at the double speak on solutions. There are no known solutions. Every solution requires a miracle that has never happened.
Kindly, I think this is where you went wrong
I share the same sentiments as you, it'd be a tragic loss. But saying they'd "end" is well, unlikely. The countries will shrink. Japan population could reach 60M by 2100 if nothing is done. That's still a lot of people and by then other factors will dominate and fertility may rise again.
Humans are adaptive and a lot can change in half a century, so I would not overly index on what projections say. Everything would need to stay static for the projections to matter, which given the rate of technological changes and geopolitical tension, sounds likely.
Yesterday I got stuck with this kind of stranger for 3 hours for work stuff. It was just me and him driving. When he started telling racist jokes and expressed his dissatisfaction with human rights I thought here we go again and went for the unauthentic route. As the conversation rolled he became more easy and personal. Told me about his family, his immigration and less nice parts of his life. I felt compassion and it really feels like we ended up being more connected than the beginning.
That's a pretty extreme change!