There are two main reasons.
Firstly, the altitude made it difficult for foreign nations being spied on to counter the SR-71. No fighter/interceptor could fly high and fast enough, and no missile could climb fast enough and track well enough to hit it.
Secondly, the air up there is thinner allowing the plane to fly with less friction. Even so, due to its immense speed, the Habu heated up so much in flight that almost the entire plane had to be made of titanium, which at the time (late 50s) was a very exotic material.
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