Why are two-port networks able to use a dependent source but not an independent source?
This restriction does not apply to a two-port network with dependent sources, why the difference as both are sources?


When you define a two-port, you're saying the network will obey a rule of the form

$${\rm outputs} = \left[ {\rm matrix} \right] {\rm inputs}$$

Where the inputs are one set or linear combination of the port voltages or currents, and the outputs are the remaining voltages or currents, and the matrix contains whichever network parameters we chose (Z-parameters, H-parameters, S-parameters, ...)

This means if the inputs are 0, then the outputs will be 0. If there is an independent source in the network, then this wouldn't be true and our matrix description of the network wouldn't be valid.

However if there is a dependent source in the network, then its output will be proportional to some linear combination of the input signals, so it can be readily handled with the network matrix description.