Current through cross coupled pairs
It's just a matter of stability, this circuit exhibits negative resistance and is hence unstable. 

Any static quiescent point is a possible equilibrium, so if you force \$I_\text{in}\$ current and \$V_\text{Y}=-V_\text{X}={I_\text{in}}/{g_\text{m}}\$ circuit will (only ideally) remain in this condition if non perturbed and exhibit the expected negative resitance.

But if you, from any such an unstable equilibrium point, try apply any disturbance, system output will diverge.

You could try a different experiment: replace current disturbance \$I_\text{in}\$ with a voltage one. 



In this case intuition (VD1 up, VG2 up, ID2 up, some current is sunk into Vin) matches math analisys.

Now system has become stable, why? What is the boundary condition?

The key point is negative resistance:

When you drive by an ideal current source, as anticipated, total equivalent resistance seen at X,Y nodes is negative \$r_\text{o}=-2/g_\text{m}\$

On the other hand driving by ideal voltage source you actually shunt ro with 0Ω internal resistance depleting negative resistance.


In between we have driving by Norton equivalent of some non-ideal generator, whenever \$R_\text{N}&lt;r_\text{o}\$ total parallel resistance \$R_\text{eq}\$ is positive and system stable.