Why the penny-farthing? The penny-farthing was the standard until the diamond-frame "safety bike" was "invented" and revolutionalized the world of bikes. 

It seems to me strange to have to "invent" to put the same size of wheels on a bike, composed of two triangles (the idea of triangles is meny hundreds of years old in civil engineering). 

Why did those awkward and dangerous bikes exist?
I think the simple reason is that the drivechain hadn't been invented. 

In 1818 the dandy-horse or draisine was invented. This was similar in shape to a modern bicycle, but without pedals. Riders would scoot along with their feet.



If you want to go a bit faster, especially on any kind of incline, then you need a better way of putting power in. Without a drivechain the only option is pedals connected directly to a wheel. The larger the wheel, the bigger the gearing. The circumference of these wheels was measured in inches and is why you may still hear gear ratios described in gear-inches.

Of course the large wheels were unwieldy and limited by the length of the rider's inside leg.