Common mode Rejection ratio
For a single common-emitter transistor amplifier, voltage gain boils down to collector resistor divided by emitter resistor. The bigger the emitter resistor the smaller the gain.

When applied to a differential amplifier (aka long-tailed pair) the common mode gain is in fact the gain of the single transistor so, if the emitter resistor is very high compared to Rc then common mode gain is very small.

Given that the common mode rejection for a perfect long-tailed pair with the output taken differentially across the collectors is theoretically 100% for any size emitter resistor (within reason), any slight imbalance in the transistors doesn't contribute a massive common-mode signal at the output but, as explained above, whatever imbalance there is will be eradicated by a high value of Re.

In fact, most op-amps (if not all?) will use a constant current source for Re and, if you did some research, you'd find that a perfect constant current source has infinite impedance.