People believe in free will because they haven't truly inspected it yet. But once inspected, the concept immediately starts to fall apart.
Most of us readily accept we're not "willing" ourselves to digest food, circulate blood, or make white bloods cells with our bone marrow. These are physiological processes, we think, and so not something we control.
And most of us will admit we didn't choose our place of birth, our parents, our socioeconomic origins, our sex or race or early childhood experiences.
We even admit (sometimes grudgingly) that we forget things. That thoughts "occur" to us. That we "lost control" for a minute and got angry, that laughter is involuntary, etc. etc. These are the most telling of all.
Yet this idea that we are in control of our thoughts and actions persists. We tell ourselves that everything listed above is "just an exception." But how many exceptions can be made until there is nothing left?
The driver of the myth of free will is both (some) religions and the social contract. In order to have God, in many cases, we need to include free will in the equation, otherwise God's omnipotence falls apart. As does soteriology, or being "saved," at least from an Abrahamic perspective.
And in order to have laws, we have to assign responsibility. Joe Smith is guilty of crime X, and he deserves to be punished.
For many people, it helps to think Joe Smith has agency, that he is in full command of his life and "chose" to do the Bad Thing. That way we can feel good about ourselves for not being Joe, and we don't have to contend with the idea that Joe is only in the trouble he's in due to pure bad luck.