mirror in frequency domain
Both the signal and the Fourier transform can be complex functions, but some interesting and useful simplifications are possible when either of these functions are purely real or purely imaginary.

when the time signal is purely real the fourier transform is said to be obey Hermitian symmetry.

\$X(-f)=X^*(f)\$

\$|X(-f)| = |X(f)|\$

\$argX(-f)= -argX(f)\$

if the time signal is purely imaginary then the fourier transform is said to be skew hermitian.

\$X(-f)=-X^*(f)\$

which will manifest itself as not a reflection but an inverted reflection.

So in short commonly used transforms and modulations will have the properties that you mention.