I’m not sure what the typical explanation is, but a transistor is not a wire.

A wire is a conductor. It conducts electricity from end to the other.

A transistor is a semi-conductor device made from semi-conducting materials, so it conducts electricity between 2 ends with a variable electrical resistance. This variable can be controlled by putting voltage on the third leg. This way a transistor is basically a resistor with a variable resistance, which unlike a resistor is also controllable by a third input.

This ability is a property of the material. It cannot be constructed by a regular wire.