For Forwards, why is it that the dividends and coupons have to be subtracted when they are an inflow and not an outflow?

The spot price assumes that you’re purchasing the asset and will receive all future cash flows.

If you take the long position in a forward contract, you won’t receive the cash flows until the forward expires; thus, you need to subtract the present value of the interim cash flows from the spot price.

Lets say you go long on one year equity forward that pays just one dividend in 3 months. You will not receive dividends. Dividends will be received by the owner of the stock. Hence you need to subtract when you want to calculate the price