bilateral feedback analysis
In this context it basically means that Zf transmits signals in both directions.

Look at the amplifier model you are using - just the amplifier, take out all the surrounding components. If you force Vo from the outside, would this produce something at the amplifier input, i.e. across Zin? No.

Now take your Zf, make the same experiment... And you quickly understand that the same thing does not apply.

A unilateral system lets signals propagate in a unique direction, i.e. from one port to another, while a bilateral system allows the signal to go in both directions.

Symmetric here means that you can swap input and output and nothing changes: if you reverse Zf, nothing changes. Think of Zf as a generic two port system. For such a system you usually have two distinct transfer functions, one from port A to port B, the other from port B to port A. If the two transfer functions are identical the system is symmetrical, i.e. its ports are indistinguishable, and if you swap them nothing changes.

This is probably stressed in your textbook because the fact that Zf is not unilateral influences the closed loop gain transfer function in a non trivial way.