Edit: You are using the false dilemma wrongly. Here's an example of a false dilemma: "Well, we need to be happy. So, do you want consumerism? Or communism? There's no third option." We can still find ways to be happy in a bad system, whether or not we engage in politics.
Original reply: That's what I'm saying. How would you know the concept of "health" if being unhealthy wasn't a thing? Same thing with happiness.
You misunderstand. You don't have to know disease to have health. However, the term "health" implies by its definition the existence of "non-health", or "disease". It's a contrast. If that were not the case, if disease didn't exist anywhere, then you wouldn't even know what "healthy" meant, because that would imply the existence of non health which wouldn't exist.
So if you want to be healthy, you must accept that some unhealthiness exists somewhere, otherwise you wouldn't know if you were healthy or not. The same way for light to exist, darkness must exist as well. You wouldn't know what a melody was without the spaces between the notes.
I'm not saying wishing to be happy is bad, btw. However, do realize you wouldn't know what happiness was if that was all you ever experienced. So being unhappy is not all bad. It will pass. The same way happiness will eventually come and pass. Don't let these roadbumps and fluctuations of emotions stand in the way of your goals, is what I'm saying.