> I'm honestly tired of these terrible analogies that don't explain anything.

Well, step one should be trying to understand something instead of complaining :)

> Single input -> discrete multi valued output.

A single node in a decision tree is single input. The decision tree as a whole is not. Suppose you have a 28x28 image, each 'pixel' being eight bits wide. Your decision tree can query 28x28x8 possible inputs as a whole.

> A neural network neuron takes multiple inputs and calculates a weighted sum, which is then fed into an activation function.

Do not confuse the 'how' with 'what'.

You can train a neural network that, for example, tells you if the 28x28 image is darker at the top or darker at the bottom or has a dark band in the middle.

Can you think of a way to do this with a decision tree with reasonable accuracy?