I'm having an issue with 2.1 as well.
They only way to get it to run, is by running the launcher-full.jar file itself, Spine.exe and Spine.com both exit immediately.
This is what the Log file has when I try to run it normally:
Spine Launcher 2.1.01
Java 1.7.0_25 Oracle Corporation
Java HotSpot(TM) 64-Bit Server VM
64-bit Java detected.
32-bit Java is required.
And this is what I get when running the jar directly:
Spine Launcher 2.1.01
Windows 7 x86 6.1
Java 1.8.0_25 Oracle Corporation
Java HotSpot(TM) Client VM
Up to date: 2.1.00
Spine 2.1.00 Professional, LWJGL
Licensed to: *, @.com
NVIDIA Corporation
GeForce GTX 760/PCIe/SSE2
4.3.0
Started.
I'm not sure whats going on, I've reinstalled several times, and reinstalled java (32-bit) too.