How does "so to speak" mean "in a manner of speaking"?

I understand the phrase's meaning and its usage, but I don't know how it could have come to mean what it does.

Similar phrases like "in a manner of speaking" and "in a sense" make more sense. A sentence like "he's a parrot, in a sense" would mean "there exists an interpretation of the statement that he's a parrot such that the statement holds true". "He's a parrot, in a manner of speaking," would mean that one might speak in a particular colloquial in which "he's a parrot" has an appropriate meaning.

On the other hand, I don't even know how to parse the phrase "so to speak": "so, [if I were] to speak, [I would say ...]"? Or is "so-to speak" a kind of speak? Or does the "so" mean "true", as in "make it so"?

Solution 1:

One of the meanings of so is 'in this way'. He's a parrot, so to speak would mean 'Speaking, as I am, in this (rather figurative) way, he has some of the characteristics of one of the fruit- and seed-eating birds of the order Psittaciformes'.