Actually its the inverse. Borrower A is borrowing the equivalent of $105 and borrower B is borrowing the equivalent of $125 and after 5 years the amount they borrowed is equivalent to $160.

Let's put this into more real terms. Lets say 30 years ago borrower C got a $100k mortgage at a 6% interest rate. Ignoring everything else that often gets lumped into "the house payment" (insurance, property taxes, HOA/condo association fees, closing fees, etc.) their monthly mortgage payment would be $599.55 for the entire lifetime of that mortgage. That $100k in 1995 dollars that was borrowed would be about $210k when adjusted for inflation. Those 360 payments would also conveniently equal out to roughly $215k meaning they effectively were loaned the money for free over the timescale, and that loan payment of $600 in 1995 is still a loan payment of $600 in 2025 despite the fact that that $600 in 1995 dollars is equivalent to about $1200 today.

Basically with inflation, property ownership ensures a roughly decreasing cost of living over a lifetime and property has a tendency to gain value faster than a dollar does, so ultimately being able to get a mortgage creates wealth for the individual by stabilizing costs that would otherwise grow indefinitely and they gain an asset that generally increases in value.