A long time ago when people first started stacking stones to make buildings, rather than just find caves to live in, it would have seemed logical that doors could be created by merely erecting stone pillars (or making openings between walls) for lintels to be lifted up onto. (the first example on left)
Corbelling over, or stepping over, one stone at a time to cover an opening may have been the next development.
Then there was the advent of the arch.
One would have thought that the 'pointed opening' would have come along first as a kind of natural progression. The pillars for an opening may have been built with a lean on purpose (or more likely inadvertently) and then the conclusion that butting them up against each other to support each other to form an opening beneath the two columns, (the second example from the left) would have seemed like a logical way to make a door. It was very structural.
A variation of this, (the middle example) where the individual stones of the two pillars angle in slightly but still come to a point, creates a wider very adequate pointed arch, later to become the Gothic arch opening. This would have no tendency to separate or slip downwards. Supporting stones over the opening would be fairly simple.
There is now a very difficult leap of the imagination in the development and design of the arch to have the insight to balance stones in an 'arc' to form a rounded or Roman arch (the two examples on the right)
This would have required more than leaning pillars. It would need more than tapered stones. The concept would be revolutionary and it would need someone to come up with the idea of a form to support the weight of the many stones which would have to 'hang' in the air until the thing was built. When it was completed the pillars would tend to separate and the stones would start to slip straight down if there wasn't proper side support. This was a lot of extra work to straddle essentially the same width opening as the Gothic arch.
This kind of rounded arch would have been a big departure from the pointed or leaning arch. It would have been developed many years after the pointed arch.
But it wasn't . The Roman Arch came many many years before the pointed arch!