The simple answer is that fluids are incompressible, whereas air (in the sub) is not. There are four phases of matter: solid, liquid, gas, and plasma. Solids and liquids have a constant physical volume, and that volume does not change regardless of the pressure. Gasses and plasma expand to fill whatever volume they are contained within, and the pressure they exert is determined by their density within their container and their pressure.

Now, a submarine is basically a metal container filled with air, and there is just enough air in a submarine to exert the atmospheric pressure at sea level. If the submarine goes underwater, the amount of air within it does not change (unless there is a leak, of course), so the pressure within the sub remains the same. The pressure outside the sub, however, is determined by the depth. As a result, you have a tremendous difference in the pressure inside the sub (which pushes the walls of the sub outward), and the pressure outside it (which acts to crush it). If the difference is too much that the net pressure is too great for the walls of the sub to withstand, it collapses.

A squid, on the other hand, contains no air; its blood is liquid and its flesh solid. It is under the same colossal pressure from the weight of the water, but since the material that it is made of is incompressible, it exerts the same pressure back, holding it up.

The secret is that the soft body does not attempt to "stand up to" the external pressure.It's really the pressure DIFFERENCE between inside and outside that crushes the sub. Imagine you and a friend on 2 sides of a swinging door. If your friend pushes on the door, even a little harder than you are pushing the door, the door will open toward you. If you are both pushing an equal amount, it doesn't matter how hard you are both pushing, the door won't move.

A sub always has a pressure inside that is about equal to the air pressure at sea level (let's call it "1 atmosphere"). If the outside is also equal to 1 atmosphere there's no pressure difference and no strain on the shell (hull) of the sub. At 10 meters below the surface, the pressure is 2 atmospheres. At 100 meters below the surface, it's 10 atmospheres, or 10 times the pressure outside as inside. In other words, a 10 meter increase in depth causes another 1 atmosphere of pressure. This can be a powerful crushing force.

The squid, on the other hand (or tentacle), has no big air space in the middle of its body. It is at "equilibrium" with the water, meaning that the pressure is the same inside and out. So there's no pressure difference, just like when both you and your friend were pushing on the door with the same amount of force.

Here are some questions for you:
If you cut big holes in your submarine and let it sink to the bottom of the ocean, would it be crushed? If I collected some sea animals at the bottom of the ocean and quickly took them to the surface, what do you think would happen?

Before I can answer your question I should first explain what pressure is. By definition, pressure is the amount of force that is exerted per unit of area on a surface. As you may know, the pressure (again, force per unit area) exerted by our Earth's atmosphere at sea-level is about 15 Pounds per Square Inch (PSI). The water pressure one mile deep in the ocean (about the depth where giant squid seem to live) averages about 2,500 PSI. So if a submarine dove 1 mile deep, every square inch of the outside of its hull would be pressed on by 2,500 pounds of force. Because the hull is sealed air-tight, the only force pressing back on the inside of the hull, against all that 2,500 PSI outside, is the 15PSI of air pressure that the sailors live in. The other 2,485 PSI from outside must be held back by the strength of the hull's metal structure.

Most submarine hulls are not strong enough to withstand such force, and would be crushed, allowing the outside water pressure to rush in and fill up the low pressure space inside.

Actually, your statement that "even the best submarine submarines can't go as deep" may not be entirely true. The US Navy is very secretive about the maximum depth capabilities of their current fleet of submarines.

See these links for examples of some very deep-diving craft:
deep-diving craft

But back to the squid. To answer your question, the reason why this same 2,500 PSI does not harm the squid is that, unlike the submarine, the squid's body is not sealed tight with a low-pressure area inside.The squid's body has the same pressure inside as the water outside. Because the squid's body is almost entirely liquid and some solid (remember that solids and especially liquids strongly resist being compressed), every PSI exerted from outside the squid by the seawater is balanced by PSI exerted on the seawater from inside the squid. There is no low pressure space inside the squid that can be crushed by outside pressure. However, if you were to suddenly bring a squid (or any other deep-sea creature) to the surface of the ocean, where the outside pressure is only 15 PSI, the extra 2,485 PSI pressing out from inside would immediately kill it. This happens because the gases dissolved under high pressure in the squid's body fluids will violently boil out under the sudden low pressure, causing massive tissue damage. This phenomenon is know to divers as "the bends", and has crippled and killed many divers who surfaced too quickly after spending time deep underwater at high pressure. This is one of many reasons why deep diving is extremely dangerous.

This is a great question... it shows you're thinking about how conditions change in the ocean with depth and how such changes might limit what kinds of animals can live there. The answer to your question involves the difference in compressibility ("squeezability") of water versus air.

Air (or gas) is very compressible, which means as pressure increases, its volume decreases greatly. To put this into practical terms: if you were able to swim down to 100ft while holding your breath (very few people can do this without passing out), your lungs would be only 12.5% the size they were at the surface! [This isn't true for SCUBA divers.]

The problem with submarines is that you don't want the air space inside to shrink to 12.5% of it's original size when you send it down to 100ft, so you have to design the outside of the sub to tolerate huge pressures without cracking or collapsing. It's just as if you were putting the submarine inside a giant trash compactor and squeezing it. Because submarines are made of metal, and metal can only withstand a certain amount of pressure before buckling or collapsing, the strength of the metal and the design of the sub determines its ultimate depth limit. In reality, a submarine pilot would never take a sub anywhere near that depth.

Why won't a giant squid - or the huge sperm whales that chase and eat them - suffer the same fate? The tissues of the giant squid are mostly made of water. The tissues of sperm whales, their predators, are mostly made of water and fat (blubber). Both water and fat are almost incompressible. You can squeeze them all you like but their volume basically remains the same. [If you filled your lungs with water and dove to 100ft, the size of your lungs wouldn't change.]

To avoid the problem of pressure, many animals that live very deep in the ocean do not have any air spaces inside their bodies (e.g. the fish have oil-filled swim bladders or no swim bladders at all). This means the crushing pressure really doesn't affect them. Pressure does affect chemical reactions, so it may change their metabolism and growth rate, but it won't cause them to collapse or shrink.

Sperm whales, on the other hand, have very large lungs. How do they survive the pressure encountered on a dive as deep as 9,000ft? Like many marine mammals, sperm whales have adapted to tolerate the effects of increased pressure when they dive in search of food. Sperm whales have a flexible rib cage to allow their lungs to collapse at depth and expand again at the surface. Imagine the discomfort you would feel if your lungs were squeezed into the size of a golf ball!

Some people compete to see how deep they can swim while holding their breath, using a motorized sled to go down and balloons to ascend. These divers describe having to get over the discomfort of having crushed lungs and saltwater invade their ears and sinuses. These divers have only managed to go about 500ft deep.