Evolution made it hurt that much for a reason; without them, our species could not proliferate. As for a specific pressure to avoid? There's no answer that question. If it hurts, stop squeezing.
I imagine that if a man tried to squeeze his own testicles the pain would prevent him from damaging himself seriously. If another man squeezed them though, I think he could probably cause irrepairable harm to these organs: they are only unprotected flesh, after all. This is why, when guys fight, there is an unspoken rule that the testicles are out of bounds. It is "just not done" to hurt another guy there.
If a woman squeezed a guy's testicles though, it would mainly depend on how strong she is; after all, we are nowhere near as strong as guys. It is well documented that a woman is usually strong enough to rip a testicle out of the scrotum, thus castrating him (try googling "Amanda Monti" if you dont believe me)
A couple of years ago, a friend confided in me that, while working as a vetenary nurse, she had squeezed the testicles of castrated dogs, which are virtually identical to a man's. To start with she only managed to permanently distort the organs, crushing the internal structure, but not actually rupturing them. Eventually she perfected the technique and was regularly able to rupture any testicle , albeit with some effort. She was of average size & build , so I would think that, in a life-threatening situation, most girls could muster the strength to do this.
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