How lines can qualify to be parallel
First, line segments must pass through boot camp. Any gay lines drop out immediately. After three decades of boot camp, they pass a test to make sure that they have never intersected. If the line segments are straight enough, then they get the badge of infinity. This lets them extend in any direction as much as they want, and gives them +5 agility.
The basic point of parallel lines is that they never intersect. This allows us to find corresponding, alternate, and total pwnage angles. A group of radical mathematicians has now challenged this, telling their noob friends that the lines actually intersect. This causes all the mathematicians not high on acid to scratch their heads, work out equations, and then commit suicide.
Real life scenarios
For things to be parallel is impossible, due to entropy, atoms, and Isaac Newton's Law of Falling (stating that a falling body leaves a dent on the floor of a canyon). In other words, at infinity, the lines intersect, while they also curve microscopically.
When lines parallel lines fall onto hard times and need to make money fast, some resort to dancing naked in nightclubs, or performing as a 'parallelograms' where they remove their clothes for money at parties.
Origin of parallel lines
Chuck Norris and Oscar Wilde decided that the universe was not large enough for both of them. When the dust cleared, they had created the impossible - parallel lines and toast. The toast was quickly assimilated into modern culture, but the parallel lines extended backwards through time, corrupting math teachers throughout the eons.