Why do you not attribute free will to the generator?

Humans naturally do it, but we can learn otherwise. So the question is, why can we learn (and then really feel) that the generator does not have free will, but the same process would not work for humans, especially for ourselves.

First, we are more complex than a random number generator. The random generator is just... random. Now imagine a machine that a) generally follows some goals, but b) sometimes does random decisions, and c) rationalizes all its choices with "I was following this goal" or, in a case of random action: "that would be too much" or "it seemed suspicious" or "I was bored". Perhaps it could have a few (potentially contradicting) goals, and always randomly choose one and do an action that increases this goal, even if it harms the other goals. Even more, it should allow some feedback; for example by speaking with it you could increase a probability of some goal, and then even if it randomly chooses not to follow that goal, it would give some rationalization why. This would feel more like a free will.

On the other hand I imagine that some people with human-predicting powers, like the marketing or political experts do not believe in so much human free will (with regard to their profession's topic; otherwise they compartmentalize), because they are able to predict and manipulate human action.

By the intra-species competition we are complex enough to prevent other people from understaning and predicting us. As a side effect, it makes us incomprehensive and unpredictable to ourselves, too. Generally, we optimize for survival and reproduction, but we are not straightforward in it, because a person with simple algorithm could be simply abused. Sometimes the complexity brings some advantage (for example when we get angry, we act irrationally, but as far as this prevents other people from making us angry, even this irrational emotion is an evolutionary advantage), sometimes the complexity is caused merely by bugs in the program.

We can imagine more than we can really do; for example we can make a plan that feels real, but then we are unable to follow it. But this lie, if it convinces other people (and we better start by convincing ourselves), can bring us some advantage. So humans have an evolutionary incentive to misunderstand themselves -- we do not have such incentive towards other species or machines.

I know this is not a perfect answer, but it is as good as I can give now.

They still cannot predict themselves, so the theory that "in principle they are predictable" still feels wrong.

Predicting humans is really difficult (when they are thinking; not when they act on reflex or habit), because very small changes in input can bring significantly different output. Trying to predict oneself is trying to predict oneself predicting oneself etc. It is like trying to understand what a difficult recursive function does.

We also have psychological fear related to predictability. Imagine what would it be like if another person would be able to precisely predict your reaction. They would be able to choose an action that together with your reaction brings them maximum utility, usually at your expense. It feels safer to insist that your actions are absolutely unpredictable. This is not related only to philosophy; in the same way people claim that advertising never works on them, or they could never become cult members. People love to pretend that there is absolutely no way to influence them. Paradoxically they often blame their failures on the environment; but they mean only economical and similar influences of environment, never psychological; at most they admit the environment has bad psychological influence on their neighbors, which in turn creates "real" problems for them. Some people even deny they could do things unconsciously; they pretend everything is a rational decision.

It is worth noting that people don't insist on having free will all the time in the same way. It is possible to convince people that they have no free will when they sleep, or when they are unconscious. It would be also possible to argue that when people are acting on habit or on addiction or in hypnosis, then their free will is weakened. And those are situations when it is easier to predict them. Having free will means having a possibility of choice that no one (including the person doing the choice) can predict. It feels like the choice is not based on laws, because a lawful choice would be predictable. It is a confusion between "I don't see a law" and "there is no law".