Why can't unequal current sources be connected in series? Imagine two power sources: PS-1 that can supply $5A$ at $100V$, and PS-2 can supply  $10A$ at $40V$. Due to conservation of charge and Kirchoff's current law (KCL), this is incorrect, and  would lead to a lot of problems to a circuit. 
But, why can't currents add up? Just like voltage. 
 A: If I understand correctly, the power that power sources output can be constant, but the current and the voltage is purely dependent on what loads you have in the circuit. Say my power source is a coal burner, that burns 5 coals a minute to produce 10 watts of power. Using P=IV, the current and the voltage can both be seemingly a wide variety of variables. However the relation V = IR must also be taken into account, so if both P and R are constants (power outputted and resistance), then the voltage and the current cannot be freely set. 
A: Electrical sources, like current sources are conventional electrical elements that behaves according to a definition.
A current source is said to impose a current. For example, when studying the circuit, you do assume that the current in the wire is chosen by the current source only. Thus, when there are two different current sources in series, you have two different values for the current. Hence a problem for your study.
However, from a physical point of view, the "current source" is made of different elements usually including coils for example. The source has an inductive behavior meaning that the current flowing through it will be continuous (no discontinuity for energetic reasons).
If you do connect two different current sources in series, the neglected elements (coils, internal resistance...) will no longer be neglectable : there will be an established current in the wire which will depend on the real operating mode of the sources. In your case, the current source is probably a regulated current source. If the current flowing through it is too big, the regulation will probably try to reduce it until saturation/destruction.
There is a rule in electrotechnics about alternating the sources (current/voltage/current) but I can't find the english name for it.
A: Would you ask why two unequal voltage sources cannot be places in parallel? In that case the answer would that infinte current would flow between them. In your case, with two unequal current sources in series, infinite voltage would be generated.
