Let's take this as two separate questions:
1. Why the expansion after the "Big Bang" is showed in cylindrical form?
Presumably you're referring to diagrams such as this:
The reason the is represented like this is because the BB's motion actually occurs in all four dimensions of space-time, but we can't represent that in a static 2-dimensional diagram. So what we do is drop one of the three spatial dimensions - reducing the 3-D spherical observable universe to a 2-D disc. Now we can use that 3rd dimension to represent time. IN the diagram above, time flows from left to right, and
this shows us how the expansion rate changed over time. The observable universe started off very small - much, much smaller than an atom - then expanded very rapidly in what is called the
inflationary epoch to a macroscopic size. Then the inflation slowed to a more leisurely rate, as it is doing today. But that rate is slowly increasing and we expect it to continue to do so.
2. Everywhere on the net, there is no image that the expansion has a departing point, through an expansion in spherical form.
What do you suppose that would look like, and why do you think it would be more explanatory than a diagram that ignores one of the three spatial dimensions?
Consider this physics projectile motion diagram:
It renders only two physical axes (x and y), even though any real world soccer kick is in all three. Do you think adding a third dimension to the diagram would add clarity to what the diagram is trying to portray?