There are two ways to lose a belief, and they often go hand in hand.
One is through friction.
I have a belief telling me how life is or should be, and an identity telling me what I am and am not. In both cases, I split life right down the middle, allowing one region of the landscape and not the rest.
When life inevitably shows up outside of my belief or identity, there is a friction between my belief and life, which is experienced a uncomfortable… as stress, something being off, suffering, anger, fear, and so on.
This friction, if it continues, slowly wears off (and out!) the belief. Over time, constantly at odds with life, it has to go, in spite of even the most persistent resistance. It is just too obvious that life is more than my belief, and I more than the identity. My personality may not like it, especially at first, but there is not much choice there either.
The other is through investigation.
I notice the warning signs of holding onto a belief or identity (stress), I identify the belief or set of beliefs behind it, and investigate its effects, what would be without it, and the grain of truth in each of the reversals of the initial story. This too allows it to fall away, although it can be faster and less painful, even fun.
In the first case, I take the side of my habitual beliefs and identities, and it may be a drawn out and painful affair.
In the second case, I take the side of life inviting the belief to go, and it becomes more playful, have a sense of more ease, and can even be fun and enjoyable.
Although most of the time, there seems to be a mix of the two. There is the friction between life and belief, and the stress and resistance that comes with it. And there is the ease of the investigation, when that is finally engaged with.