Under the current nebular model of solar system formation, we began with a big cloud of gas and dust, which began to collapse (probably after some sort of nudge from passing star or shock from a supernova or the like).
This cloud almost certainly had some slight rotation to it, as it’s nearly impossible to get an extended cloud without any. As the cloud collapses, it’s difficult for it to collapse towards the axis it’s rotating around because of the conservation of angular momentum–when you try, it just spins faster, like a figure skater pulling in their arms. This doesn’t apply to the parts of the cloud collapsing “down” parallel to the axis, so the cloud flattens out into a disk.
For a vaguely similar model, think about someone making a pizza–they start with a big ball of dough, but they spin it around and it ends up flattening into a disk, not just compressing into a smaller sphere.
Note that there are some parts of the cloud that didn’t collapse down like this, and are still out there in spherical form. We call this (hypothesized) part of the solar system the Oort cloud.
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