For example, you can't decide to see the color blue, but it is very likely that an AI equipped with light sensors could decide to directly provide input to itself as if its sensors were seeing the color blue.
Emotions may (or may not, we don't really understand the working of the brain well enough) work similarly. There may be brain 'circuits' that provide inputs to the part of the brain that creates consciousness that represent emotions. We don't have a way to really 'fake' these internally, but an AI perhaps could. And of course, it is very difficult to imagine how a being that can just choose to be happy in any circumstance would actually think and react to the outside world.
Once I have seen it I can always visualize the color blue because color can be stored in memory and IMO that is why computers can describe color. But even if I was once happy I can never visualize being happy I just have to experience it and that experience/ substance of happiness cannot be encoded.
Not to mention, there are people who at least claim they can feel at least certain emotions, such as serenity, regardless of the situation that they are in. It may be that with enough study, we ask could actually learn of a way to feel happiness regardless of external context.
Emotion: a process that involves cognitive interpretations of your context (environment + thoughts) and a physiological feeling through the senses (heart rate, tingly sensations, weird feelings in eyes). Check out the James Lange theory. There are better theories, but this has the fundamentals.
I ad libbed this one, I wanted to show that there is a difference. It wasn't my intention to be pinpoint accurate.
Computers can do math too. QED: your argument makes no sense.