In 25 words or less, can anybody explain why weather forecasters always say: "rain (or snow) is falling?"

The weather person is setting up an image in your head by putting it that way. It's more vivid than saying "There's rain in the area right now." And you have to room to say "heavy snow is falling in the Northtowns." Or whatever.

I've seen snow and rain blow sideways. It's a scary sight. I'll take falling anytime.

because either "falls" to Earth from the clouds...

Rain is a type of precipitation, a product of the condensation of atmospheric water vapor that is deposited on the Earth's surface. It forms when separate drops of water fall to the Earth from clouds. Not all rain reaches the surface; some evaporates while falling through dry air. When none of it reaches the ground, it is called virga, a phenomenon often seen in hot, dry desert regions.

It's a discription. English is a colourful language! It's done that way so even a Scheisskopf or football fan (is there a difference?)can understand it.

Rain or snow is rising? Ahem.

Could be because they don't know how to use 'ing' or could be because they have more time and need to use it up by adding more in their dialogue.