Greenhouse gases only interact with specific wavelengths of light. A lot of sunlight comes in as visible or ultraviolet light, mostly passing through those gases. It hits the surface of the Earth and is absorbed and then re-emitted as infrared light, and a lot of that is just the right wavelength for greenhouse gases to interfere. Here's a good article about the physics of this: https://www.quantamagazine.org/the-quantum-mechanics-of-gree...
Basic greenhouse effect: Visible light (and ultraviolet light) comes in relatively unhindered. Gets absorbed by the earth and heats it up. The heat is emitted as infrared radiation. This gets absorbed by CO2 (and equivalents) and reemitted in a random direction. Takes a long time to reach space by chance, so the energy stays in the atmosphere for a while.
The radiation on the way in has a different frequency than on the way out. For example, there is UV included in sunlight. But black body heat at Earth's temperature radiates in infrared. Clouds are very opaque to infrared, and more (though not completely) transparent to UV.
This is the actual answer. The clouds aren't differentially reflecting sunlight into and out of the atmosphere, they are reflecting the black body radiation emitted by the earth.
Single particles of radiation coming from the sun have higher energy than single particles radiating from the earth. Even though the total energy entering and leaving earth is at a near equilibrium.
My mental model is that a bullet leaving the barrel of a gun has much more penetrative power than that same bullet once it has ricocheted off a concrete wall.
Because it comes in at a different frequency versus when it goes out. Light, including UV and visible light, hits the ground, then the ground gets warm and radiates in the IR, which can be blocked by clouds.
