Between the two screws where the black and red wires are, there is a metal tab connecting the two terminals together. Remove that tab by cutting it with wire cutters and you will have the switched half back again. Do not cut the tab on the side where the white wire is, only the hot side needs separated for a switched outlet. The white (neutral) wire serves both halves of the outlet.

Some of the tabs have a slot for a small screwdriver blade to be inserted.
The screwdriver is then used to rotate the tab until it breaks free at both ends.

..others you bend back and forth until it breaks off.

OP says he has two white wires, could he have 2 circuits there where each one needs its own neutral?

If so, he has to also cut the tab on the white side and use both white wires.

Either that or they used the receptacle to feed the neutral through to the next one in the circuit. Best bet would be to inspect the receptacle he replaced.