Here is the circuit we understand you to mean when you say "two currents in series":
simulate this circuit – Schematic created using CircuitLab
For I2 to be a 2 A current source, 2A must be flowing in to its left terminal and 2 A flowing out of its right terminal. But for I1 to be a 1 A current source, 1 A must be flowing in to its left terminal and 1 A flowing out of its right terminal.
That means 1 A is flowing in to node A from the left but 2 A is flowing out of node A to the right. And no other branches connect to node A.
What your book means by saying "KCL will be violated" is if you form a KCL equation at node "A", you get
$$1\ {\rm A} = 2\ {\rm A}$$
which is a logical contradiction.