Everyone believes that they have a soul, the contention is the nature of the soul. You have an intangible essence which inhabits your body, and you identify with your "self". Some people think it's some kind of immortal ghost that gets to live in the clouds with other immortal ghosts when the body dies, some people think it's an emergent phenomenon of some variety which disappears when the body dies. These are differences in explanation, secondary to the ontological question of existence.
The "I" in your statements is proof of your soul, any disagreement is really just pedantic quibbling over terminology because you believe the term has been tainted by explanations you don't agree with. Even if your brain is "making it up", it's still a phenomenon. Your subjective internal experience is made of "soul", your concept of self is made of "soul". The entity asking the question and reading the responses is your soul, simple as.