The reason is quite simple: the contents of our bodies (blood, bones, muscle, etc) are at the same pressure as the atmosphere.
Even if they were not, atmospheric pressure is certainly not enough to get our bones crushed. When a diver is 10m under water, the pressure is doubled (202650 Pa). Any recreational diver can do that. I have been deeper than that, without any ill effects. At 100m, the pressure is 10 times atmospheric pressure, and only specially trained divers, with special equipment (including breathing gas that has nitrogen reduced and replaced by some other gas like helium) can go there. Thedeepest verified diveis 318m - about 32x atmospheric pressure.
Fish and other marine creatures have their internal body pressure the same as the water around them. As a result, even in the deepest oceanic trenches there is life.
The reverse is more dangerous. If our body was exposed to vacuum, the internal pressure would quickly kill us, as explained in thisquestion.
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