I wonder if this question is actually based on Guns, Germs, and Steel, by Jared Diamond. I have two reasons to think this. First, Diamond is very interested in the power of steel weapons and he wants to know why some regions of the world had them before others. This means that this question would be very relevant to him. Second, I do not believe that Europeans really were the first to have steel swords. The link below suggests that steel swords originated in India. It is clear that Eurasians were the first, but not that people in Europe were the first. So I wonder if this question is really meant to ask why people from Europe had steel swords while the Incas did not (this is relevant to Chapter 3 of Diamond’s book). I will base my answer on Diamond.
To Diamond, Eurasians got steel technology first because they had civilization before the people of any other continent. Eurasians had civilization first because they developed farming before anyone else did. They developed farming first because they had good geographical luck. This is the main point that Diamond tries to make in his book.
To Diamond, farming comes about because of geographic luck. Farming develops in places where there are many plant and animal species that can be domesticated. It diffuses rapidly along east-west lines because growing conditions are similar in places around the same latitude. The Fertile Crescent in Southwest Asia had many plants and animals that could be domesticated which helped cause farming to develop there. Eurasia has a long east-west axis, which helped farming spread to other parts of that land mass.
As farming spread, so did civilization. When people farm, a few people can raise enough food to feed many people. The people who do not have to farm can spend their time doing other things, such as developing technology. Therefore, people who have been civilized the longest are most likely to develop any particular technology. This is why Eurasians were the first to develop steel swords.