Under the Roman Empire, soldiers were supplied with their arms and armor by the state. These were initially produced within forts and fortresses, and were later made in centralized fabricae. This material was mass produced and made to a high standard. As the Empire transitioned into the Medieval period, these factories dissolved, leaving private smiths to produce the material which was certainly more expensive. Swords became a status symbol of rich warriors, as they had been in Iron Age Europe or the Bronze Age Aegean earlier. If you are interested in reading more, Simon James' latest book "Rome and the Sword" is a good overview.

God, the misconceptions on the Middle Ages in this subreddit actually make me mad sometimes. Stop reading 50 year old books about kings and knights and start learning about actual everyday folk! Chivalry didn't exist outside the minds of chroniclers! Knights were grubby, dirty people who were usually far less literate and refined than townie merchants! Start reading social history, people.

Swords were very common and easy to come by in the Middle Ages. Just as much or even more so than during the Roman period. Let's really not pretend like the Romans had either advanced trade connections or advanced technology. They didn't. Europe in 1300 dwarfed the Roman World in terms of population, trade, and technology.

We know weapons were common because:

1. most rural men had obligations to fight for their lord as part of their duty.
2. Generally speaking, families were expected to defend themselves and their houses. If someone was breaking into your house, you couldn't call the police. You couldn't send a kid running miles away to bang on the Lord's castle's gate. You dealt with it yourself.
3. There were laws prohibiting carrying weapons into cities, suggesting most people were armed on the roads
4. likewise, Laws might prohibit Jews from carrying weapons here or there, but make exceptions for travel or other circumstances.
5. You wouldn't walk around a city at night unarmed, generally speaking
6. Court case after court case, document after medieval document, contain crimes of homocide or injury by bladed weapons. The archives are full of them. I've seen them.
7. Specific Example: Rural peasant warriors called "Almogavers" joined the invasions of Peter III of Aragon after the Sicilian Vespers. They each came with their own sword and a couple of javelins.

Moreover: The Steel of the Middle Ages was of a markedly higher quality than during the Roman period. Metalworking advanced greatly during the medieval period, mostly under Muslim-ruled areas. Remember, the Muslims inherited the best parts of the Roman Empire: Alexandria, the Levant, and later Anatolia. They also inherited the best parts of Persian, Arab, and Indian civilizations too. Damascus steel was said to be some of the best in the world, inherited from ancient traditions in India and China.

Medieval trade routes dwarfed the Roman ones; make no mistake. By the 14th century there were far more people in Europe (pre-black plague) and far more boats going to and fro. Yes, trade still linked India with England. Yes, weaponry and technology was traded among Christians and Muslims.

EDIT after reading all the replies. Main Source: PhD (ABD) in Medieval mediterranean trade and piracy.

I don't know if I can answer this question completely. I'm not sure I'm aware of what context this claim comes from and I haven't come across this specific statement myself, so some of this answer borders on speculation. All the same, maybe I can provide some background for why this might have been so.

Under the Roman Empire, at least after the Marian reforms, the army was a state institution and was paid for by the mechanisms of the state. This largely involved wealthy individuals fronting money to equip their soldiers, but the important bit is that the soldier did not need to provide his own kit, as was the case during the republican period (indeed, in most ancient armies candidacy for service rested on whether one could afford to arm himself and with what, e.g. Roman Republican Equites consisted of those families who could afford to keep and ride horses). I'm half remembering a quote by Crassus (I think, I'm at work only a couple of books on hand) in which he said something like "A man isn't rich unless he can afford to raise his own army." After Augustus, the army as an institution was really solidified as a state enterprise and was the primary expense of the empire.

There's also the matter of trade. At its height, the Roman Empire completely encircled the Mediterranean sea, which facilitated a great deal of trade within the empire (grain from Carthage and Egypt, oil from Spain, etc.). Most simply, there was a uniform currency (though barter was still common), but also the ultra elite held lands and industrial interests throughout the empire. It was a relatively unified economic body. This may have been a contributing factor to keep costs of arms and armaments down in some of the same ways that trade does now (though modern trade is LOADS more complex).

By contrast, the middle ages (particularly the early middle ages) were characterized by a fragmenting of this political and economic unity into a number of separate polities (Visigothic Spain, Frankish Gaul, Lombard Italy, etc.). These were often at odds with each other and among themselves (the Merovingian Franks come to mind). Among other things, this has an effect on trade, particularly in refined goods, i.e. arms. I don't recall reading anything particularly pertaining to reduction in availability of arms, but more to a general simplification in material culture in Europe in the first few centuries after Rome. Another note - accounts of army sizes from the Roman era number in the tens of thousands of men, whereas in antiquity they tend to top out at a few thousand. I'm not sure whether this is a cause or effect.

I'm not sure I can source all the books that I'm drawing from, but the part about material culture comes from The Inheritance of Rome: Illuminating the Dark Ages 400-1000 The rest of my books on Rome are at home and I can source them later if necessary.

Roman soldiers (At least those of the late republic) were supplied iron arms and armour by the state, rather than having to purchase it themselves (as many medieval and other ancient-world states required their populations to do). For example under the Norman kings, Englishmen were required to purchase and maintain various pieces of equipment in regards to their social status, which inevitably lead to poor men owning only a spear, padded coat and an iron cap, which they would hand down through the generations.

It is also important to note that the Romans had a massive mining industry that wasn't matched until perhaps the early modern period. This industry was fueled by thousands of slaves that the Romans had acquired throughout the ancient world- something that medieval states by and large did not have access to.

So to answer your question, Swords were less common in the middle ages because of both the lack of a strong centralized government (with a well-funded, standing army) and because iron was harder to come by due to the lack of a strong mining industry.