Antisymmetry of final State Requiring L = 1

I'm currently trying to solidify the notion of parity conservation in my head and saw this example on wikepdia, and am just wondering why in the reaction d + pion- ---> n + n (where d is a deuteron)

"Using the fact that the deuteron has spin one and the pion spin zero together with the antisymmetry of the final state they concluded that the two neutrons must have orbital angular momentum L=1"

Why does the antisymmetry of the final state require that the angular momentum = 1?

See the example on wikipedia here,
parity = (-1)^L

we must have L = 1,3,5...

but only L = 1 is compatible with angular momentum conservation

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