They will not go up enough to make your claim valid, full stop. It has never happened in the way you've been claiming, so you can't even point to the historical data to back yourself up, it seems.

Inflation is not something that needs to be included in this, and it only hurts your case further. Your original claim is that if interest rates go up (now you're saying "a lot", but it doesn't change anything), home prices go down.

Well, in the 80's, interest rates went way up, but housing prices didn't go down, even in the short time period where inflation isn't going to meaningfully be a factor. It went up at the a slow rate. So, you're grasping at straws now ("correct the second for inflation" even though it didn't magically make the housing prices go down in any way that matters) seemingly because you didn't understand basic econmics in the real world and dug yourself too deep.

Are you going to provide any sources for your bold claim? Any amount of data? Anything? Or are you just going to keep talking in circles and not providing anything of substance?