Intuition behind borrowing the profit today (payoff*e^-rT) from long short or short long.

Which at the expiration will equal to the payoff that we should be getting from our positions. Doesn’t we have to payback the borrowed money so where is our payoff

The payoff is today. The arbitrageur will borrow the profit (which would otherwise have been earned in the future), therefore bringing the profit back to today instead. The arbitrageur will then pay back the borrowing in the future, which will net off against the future cash flows.

Basically, the future payoff will net off to zero, and the payoff today will be the borrowed profit (PV of the future profit).