Rain comes from clouds which are thousands of feet up. Humidity is measured in the air at ground level. 100% humidity is often associated with fog, mist, dew — water that comes out of the air near the ground.
The rain from clouds is sometimes associated with “cold fronts”… or cold air masses pushing against warm air masses. The air with feel cooler after one of these fronts pass through. Not all rain is caused by that. Some are caused by warm fronts (warmer air coming in). There can also be a temporary increase in humidity from evaporating puddles.
100% humidity means the air contains as much water vapor as it can hold. That means no additional water vapor can be added. That does not mean existing water vapor will spontaneously condense and fall out as rain.
Imagine an empty box. It can fit so many things. Once it’s full, it’s full, but that doesn’t mean the things that are in it are just going to magically jump out of it just because the box is full.
In order for rain to happen, that water vapor must be condensed into water droplets, which usually happens as result of a drop in temperature (usually because the water vapor has risen to a certain altitude), those droplets continue to condense and combine until they are too heavy to be held aloft upon which they fall as rain.
On a hot and humid day near the ground, that’s not going to happen.
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