How can metals be so strong, when metallic bonds are generally weaker than ionic or covalent bonds?
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Metals are not really strong in comparison to other materials. They are however very cheap and easy to work with so they make for a good compromise between price and strength.
The problem with covalent bonds is that there is a limit to how large you can make the molecules. With steel we easily make crystals of millions of tons which have the same strength throughout it. But the largest molecules of covalent bonds are just a few thousand atoms. Between the molecules you have much weaker interactions. So when you make strong materials from covalent bonds you need to take very much care to maintain the contact between the molecules, the forces within the molecule is strong enough. This is how we can make ropes that are much stronger then steel, but at a much higher price. But even then if you try to compress the material the molecules are free to move around in relation to each other.
As for ionic bonds these are very brittle. While we can make very large crystals these crystal structures are extremely rigid, unlike metal crystals which allow the atoms to move within them. So when we apply force to a crystal made from ionic bonds all the forces go through one bond, and unlike metal it does not move and will try to contain all the force on its own. And when you break one bond the load is applied to the next one and so on. So the ionic bonds have trouble working together like the metallic bonds. Again you can make use of it though. Concrete is ionic bonds and is much better at withstanding compressive loads due to its rigidity.
What we can do is combine different materials to get the benefits of covalent and ionic bonds. This is often what composite materials are. For example fiberglass and carbon fiber. These can be much stronger then any metal but is more expensive as they require a lot more effort to make.
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