Short a bond future. How to gain from it?

I have read that if you’re short a bond future you gain from a gain in interest rate.

Can anyone explain the logic behind?

Thank you.

When you take a short position, you are hoping the price falls. When you short, you sell high, and hopefully buy it back at a lower price. When interest rates go up, the price of bonds go down. A short position on a bond is a winner in that situation.

Lets see if u agree with my reasoningn:

I see it as being short as having the obligation to give back a bond lets say for USD 100. (So i need to buy it in the future)

If I can buy it in the future at a lower price (interest gain) I would benefit from it.

borrow money to buy a bond and sell a future high.

in the future :

deliver that bond via the future at the high price you agreed.

Pay back the money you borrowed initially - at a lower rate

the difference is your payoff