It only seems strange to you because you've had the benefit of never having to learn the lessons of the penny farthing and the technological achievements of the safety bicycle firsthand (aka 'standing on the shoulders of giants syndrome').
The penny farthing is only awkward and dangerous because you are comparing it against a technological leap forward. That technology you are taking for granted, and are not realizing just how difficult it was to develop those technology without having the advantage of already knowing about it. Two of the key pieces of technology in a bicycle you are taking for granted:
JamesBradbury's answer shows the dandy horse.
- Pneumatic tire: rubber tires didn't exist until 1887, when John Boyd Dunlop invented them. Without pneumatic tires, the ride from a smaller wheeled vehicle would be awful compared to a penny farthing.
- The chain - The humble, tiny roller chain requires a significant amount of manufacturing sophistication to be made affordable. A bicycle chain has around 500 individual parts that all have to be precisely fit together. Mass production was a fairly new concept, and really only began in the 1850's and first being effectively used during the US civil war. Importantly, the chain wasn't invented until 1880.
The safety bicycle had some initial problems of its own too, it began with a treadle bicycle, prior to the inclusion of the chain drive.
Additionally, the idea of "triangles" and their use as structural members isn't as old as you might think. Sure, people have known for a long time that triangles are 'strong', but our analytical and mathematical knowledge of them is only since the middle 17th century.
So the bottom line: people rode penny farthings because the modern bicycle wasn't invented yet.