Apparently proving the Collatz conjecture would be one of the greatest achievements in mathematics, because it is extremely hard.
How do we know it's hard before it's proved? Why can't it (e.g.) be easy, given some as-yet-undiscovered technique? Zeno's Achilles & Tortoise paradox, for example, appears to be difficult until one discovers that it's possible to ascribe a finite sum to an infinite series.
I'm looking for an explanation as to how we know a problem (not necessarily the Collatz conjecture) is hard before knowing the solution. Presumably "people have thought about this for a long time but haven't been able to solve it" is an indication, but it's still not a conclusive one, since people also thought about Zeno's paradoxes for over a century before they discovered infinite series can be summed.
Edit (by DD ~ I hope this is okay!)
Please explain to me why certain well-known open problems are extremely difficult to solve. Some examples or your own well-defined metric of hardness will do.