"that's sad" usually means literally, "that's sad".

How the other person interpreted it ("that's dumb") is more of a slang usage.

It's like, "It's sad that you would be the kind of person who'd do that". It's heard as a personal judgment, and not a judgment about the world or the situation.

One of those...backhanded statements that passive-aggressive people would use to make it sound like they're judging a situation when they're actually judging a person.

I don't think you did anything wrong. If you want to avoid that misunderstanding in the future, you could clarify what about it is sad.

"It's sad that raising children is seen as prohibitively expensive where you live". Tons of words, I know. That's why I'm not blaming you for what you said, lol