From Wigner's theorem, we get that a physical symmetry can be described either by a unitary or antiunitary operator, eventually with a phase factor, as in here.
However we have to respect the group structure, so we need to have:
$$O(f)\circ O(g)=e^{i \cdot\phi(f,g)}\cdot O(f*g)\tag{1}$$
where $*$ is the group operation.
For unitary operators this is fine, but for antiunitary operators there is a problem: the left side of the equation is linear while the right side is antilinear.
Here my doubt comes. The argument of linearity is used to show that only unitary operators can describe continuous symmetries (e.g. spatial translations), but why does it not work for symmetries associated with a finite group (e.g. time reversal)?
I'm not asking why time reversal needs to be described by an antiunitary operator, I'm asking how come an antiunitary operator can satisfy $(1)$ if it's the representation of a finite group.