why is it more beneficial to enter as the fixed-pay side of a swap when the swap fixed rates increase? in the contrary, why is it good to enter as a fixed receiver when fixed rates decrease?

If fixed rates are on the rise, you can lock in lower fixed rate, and receive the higher floating rate. That just seems to me like a good plan to me.

If you’re pay side, you lock in a fixed rate. If rates increase, you still pay that same fixed rate, so you benefit. If you’re receive swap, you receive a fixed rate. If rates decrease, you are still getting a higher fixed payment than you can get in the market currently.

alright so basically you ride the wave, i.e. rates are increasing, lock on a rate and enjoy the ride and vice versa!

Simple as that! You can make as much money as you want.