In England c.500, every farmer owned a spear. They used them around the farmyard: to herd cattle, to drive off deer, as a walking stick. They cleaned their blades often, wearing the edges down to a gentle concave curve. They took spears to the local assembly, where they listened to complaints and made decisions with the other farmers from the valley. Sometimes a dozen men carried their spears to a neighbor's house and demanded he make good on a broken promise, or suffer the consequences. Perhaps once a year, they would go far from home: perhaps on a raid for slaves, or to drive cattle across country to trade for other necessaries with the farmers a few valleys over. When they met at parties, weddings, and festivals, the young men brought their spears and showed off in front of each other. And when they died, many would take a spear with them into the ground.

A few people had swords. These were rare things; each blade took a hundred hours to forge, and its metal had to be of the highest purity. The blades were made from dozens of thin bars welded together and twisted to make complex patterns. Only the best, or the most careful, smiths could forge a sword. A few men had them, and some were even buried with one. Some of these men claimed to be better than their neighbors; some were just rich.

Most people didn't bother, because a spear was lighter, faster, and more useful. Spears weighed about a pound, were carefully balanced, and wickedly nimble. A sword could split open a man's skull if the blow landed, but a spear could stab a swordsman three times before he could get a second swing. A young man with a spear was like a minnow, except with teeth. Some people think spears were just for massed figting rather than duels, or didn't do much killing on their own--these people haven't handled the spears from c.500 England. They were rapiers, only made from wood and iron instead of steel.

By 600, some farmers had done well for themselves. Through luck and hard work--but mostly luck--they had managed to stockpile some wealth. They built larger houses, and wrangled obligations from their neighbors. They hosted large parties in these houses, and some called themselves kings. As the century went on, they grew more and more rich, and started to outfit professional warriors who took on more and more of the duties that spear-wielding farmers used to bear. In exchange, the farmers paid a bit of their surplus to the big houses, to feed the warriors (or 'bread eaters', as one law code called them). These warriors were serious about fighting, and they had cash to spend on their gear. Many invested in swords, alongside their spears. These weapons, alongside their larger, heavier war-shields, marked them as a new military elite. Farmers still owned spears, and that wasn't anything special--it was the swords that set the elite apart.

By the eighth-century, hero stories were beginning to be written down. In these stories, we see both swords and spears, as well as helmets, shields, and knives. The spears are associated with the followers, and the swords with the heroes. The exploits of the new social classes--professional warriors with their famous, sometimes named swords--were preserved on parchment, and the farmers were forgotten. Western Europe never turned back.

Spears never stopped being important. What was the high medieval knight's iconic weapon? (A lance.) spears never stopped being common, either. And spears were magical--they were made from wild trees, and often from specially selected iron that was chosen because it came from a famous person, place, or event, and these materials gave them qualities that early medieval people saw as demonstrating life. Spears were thought to be capable of learning from their experiences, taking power from people they killed, and becoming dangerous and difficult to control if they were used too long in a bloody, endless feud. People were afraid of some spears, and carefully broke their shafts and melted their blades to ensure they could cause no further harm--something rarely done to swords, in England at least. (King Arthur had a magical spear, you know, in some of the early stories).

The details of this story vary outside of England, but the outline remains the same. Swords were harder to make, harder to buy, and more closely associated with professionals rather than casuals. A spear was useful on the farm as well as in battle; a sword was only ever useful for warriors. And who are our medieval epics about? Not farmers.

Not to discourage new answers, but u/alriclofgar and others answered a similar question here. If you are interested in Swords' specific place in society in late medieval Europe, I discuss this here.

Am I missing a hidden cultural history on Spears?

Um... the bayonet? It was the tactical successor to the spear/pike, and was also the replacement for the sword as a backup sidearm for the infantryman.

Sword bayonets in particular (late 18th through 19th C., even longer in the Japanese Imperial Army) were quite literally a fusion of sword and spear. The spear-like functions tended to be more tactical, while the sword-like functions were actually more likely to be applied as a tool for chopping, digging, brush clearing, etc.

Otherwise, lots of great discussion in this thread, but it seems to be inordinately focussed on early medieval history. The spear (and relations like the pike) retained a military prominence for another thousand years after that, so it doesn't strike me as getting to the heart of the question, which (as I read it) is why did the spear disappear as a cultural icon? But just looking at the prevalence of bayonets on WW1 and WW2 propaganda posters like this I'd argue that it didn't. It just morphed into a form that got a different name.