Why is connecting two different voltage sources in parallel dangerous?
As a conceptual model, a voltage source maintains its specified voltage even if doing so requires the supply of infinite current.  Obviously that is not a component you can buy.

Connecting two set to different voltage sources with non-resistive wiring breaks their definition, so is an unanswerable problem.

In the real world, many devices can be approximated by the Thevenin equivalent model, which consists of an ideal voltage source in series with a resistor representing the internal impedance and response of the non-ideal source to load (there is a dual, the Norton model, which has a shunt resistor across a current source).  

If you interconnect Thevenin or Norton source models, you can use basic circuit analysis to calculate the results. 

Components such as batteries may be imperfectly approximated by these models.  With care they can give you some idea if you are likely to run down, (over)charge, or explode interconnected parts but for obvious reasons it's an area where you want to allow huge safety factors.