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Look at it more like this. Say I tell you to pick any number, square it, and then add 5. Say I did this and my answer was 41. What was my original number? 90% of people will answer 6, but my answer was -6. Now only doing that once isn’t hard, but basically it’s because the inverse of the function is not a function that I can’t always get back to it. Now do that a few thousand different ways in the same problem and good fucking luck.
While it’s not what is happening as it’s using pairs of primes, it’s an easy way to explain there’s not always a way to get to something from an equation.