The interesting thing about steel is that the tiny grains that make it up are immensely strong, far stronger than any other material we have.
But we have no known method of making steel out of just those grains, it's always mixed with other weaker parts.
That's why spider silk is so incredibly strong - it's manufactured (essentially) one atom at a time.
If we could manufacture steel in the same way it would be far stronger than spider silk.
Here's a list of some of the various grains in steel:
Pearlite, Cementite, Bainite, Austenite (there are many more).
The steel making process is all about encouraging a specific type (and especially, mixture) of these grains to form. But we can do so only at low efficiency and in a random fashion.
This is partly misleading. It's accurate that steel is made up of grains, analogous to grains of sand, but the things you mentioned are more correctly phases, several of which can exist within a grain.
e.g. Pearlite, which you mention, consists of two phases, cementite and ferrite. And these phases can form at the edges of grains, or within grains, depending on growth conditions.
But this isn't the important thing. The important thing is that it's meaningless to talk about how strong "single grains" can be, and how wonderful it would be if we could make large single crystals. And it's meaningless for two reasons: firstly, there are always trade-offs. If you make a large single crystal (i.e. a single grain) you'll sacrifice toughness, because cracks will be able to easily propagate straight through the crystal, without any grain boundaries to stop them. And secondly, you have entropy. Whenever you try and make a large version of something small, entropy dictates you will always have defects. This is why, for example, carbon nanotubes will never scale (which is not to say they won't be useful, they will be!) but if you try and make a centimetre long nanotube it'll be full of defects and will never, ever, be as good as a single microscopic nanotube which is almost perfect.
Anyway, the point is, there's no perfect material. No "good parts" and "bad parts," there's always a trade-off. Sometimes the "bad" parts can do very useful things. As an example, if you make a very strong steel, good luck trying to shape it into anything useful! Imagine if you have a lump of the "best" material in the world, if you can't find a chisel to carve it into something, then it's not going to do anyone any good...
And claims like those given in the parent article are always a little dubious. It's hard for people to imagine the scale of the steel industry, and I personally know of processes that are great in the lab for both steel and other metals which have wonderful efficiencies but just can't be scaled. A kg of steel should cost about the same to make as a bottle of water. If the equipment/size/energy-to-run-equipment investment is just a little too high per kg, it's not going to be useful for anyone at the kinds of scales it needs to be...
That said, despite the difficulties there has been huge progress made in the last few decades, and this might be one of them! Without more information I couldn't say (and it's not my area of expertise anyway), so I wish them luck.
Loosely stated, imagine that atoms can be arranged in a very large number of configurations. Only one of those will be "perfect", i.e. a perfect crystal structure. The rest will be defected in some way or other. As the size of the system increases, the amount of defected configurations also increases and the greater the chance it will have a defect. This is due to entropy/thermodynamics, depending on your interpretation.
That's it in a nutshell, I'm sure someone else can clarify.
But we have no known method of making steel out of just those grains, it's always mixed with other weaker parts.
That's why spider silk is so incredibly strong - it's manufactured (essentially) one atom at a time.
If we could manufacture steel in the same way it would be far stronger than spider silk.
Here's a list of some of the various grains in steel:
Pearlite, Cementite, Bainite, Austenite (there are many more).
The steel making process is all about encouraging a specific type (and especially, mixture) of these grains to form. But we can do so only at low efficiency and in a random fashion.