Each team has its own footballs.
It one team deflates its footballs and the other team doesn’t do the same to its, there is a decided imbalance.
A deflated football is not only easier to catch, it is easier for a runner to grip and easier for a passer to grip and throw.
When a team is on offense its footballs would be used.
I had the same question. I had no idea that each team plays with their own set of footballs.
Now that I know, I am left with the thought, “What an incredibly stupid idea. Why not use one set of footballs for both teams to ensure parity?”