I have no idea if someone has already worked this out, and I'm not going to bother checking, because the explanation is fun and simple. You may have already worked out what is going on yourselves; if not, this will be quick.
I start by noting that Modern Greek is pretty impoverished when it comes to prepositions. In contrast to the prodigious combinatorics of prepositions and cases in Ancient Greek, and the neurotically precise locative adverbs of Pontic, Standard Modern Greek makes do with very little: από for motion from (or distance from), σε for motion to (or proximity to), and a few adverbs for clarification. Ancient Greek could deal with motion past by a simple παρά; but that is not available to the modern language.
So with the limited means of "from" and "to", Modern Greek needs to convey a notion of a temporary destination. What it does is not particularly uncommon in colloquial, vivid language: it has come up with an expression that is economical, but that is not the obvious way to say it. That is what makes it vivid language, the first time you see it: like a punchline to a joke, you have to think about it to get it. The expression conveys the notion of a temporary destination, which will then also serve as a point of departure later on. So X is both a destination and an origin.
To achieve this, X is marked as a destination in one way, and an origin in another way. It is marked as an origin by the preposition, "from". It is marked as a destination by the context, because the expression only works if you're not already at X. That's what makes you have to think about it, in classic punchline mode—that is, in conversational implicature:
- Πάμε από την Πανεπιστημείου "We're going from University St"
- But we're not already at University St
- So we're going to have to go *to* University St, so we can then go *from* University St to somewhere else
- So we're going to stay at University St only briefly: we're going past University St
You also use this expression to emphasise this X is part of a route: you go to X precisely in order to get to somewhere else, so X is the origin for your ultimate destination. Hence Tipoukeitos' example:
- θα πάμε από Πανεπιστημίου γιατί η Ακαδημίας είναι κλειστή "We'll go *via* University St because Academy St is blocked off."
In fact από "from" is the way Modern Greek expresses "via".
Now expressions like this, with odd prepositions after verbs, work by analogy with other verbs. Prepositions are quite flexible in their meaning, according to the verb that governs them: English prepositions' meanings are so hard to pin down because they are determined by verbs.
There is a verb where "from = past" is already well established in Modern Greek, and it is of course περνάω, "to go past, to go through". In fact, "from" after περνάω has the same shade of meaning there as well, compared to the normal expression:
- Πάω στην Πανεπιστημίου "I'm going to University St"
- Περνάω την Πανεπιστημίου "I'm passing through University St"
- Πάω από την Πανεπιστημίου "I'm going past University St"
- Περνάω από την Πανεπιστημίου "I'm going past University St"
Normally, you go to (πάω σε X) a destination; by saying "from", you're making the destination an origin as well. Normally, you go through, or overtake a tangent (περνάω X); by saying "from", you're making the tangent an origin—which implies you're stopping by there long enough for the tangent to become an origin. If you don't say "from", X remains a tangent, and you can't be stopping there:
- Πέρασα από την Πανεπιστημίου να δω το Γιώργο "I went past University St to see George (at University St)"
- Πέρασα την Πανεπιστημίου να δω το Γιώργο "I went through University St to see George (at the next street)"
Cf. Tipoukeitos' example:
- θα πάω απ' την πεθερά μου πρώτα να πάρω τον μικρό "I'll go by my mother-in-law's first, to pick up the kid".
And because περνάω/πάω από is strongly associated with places as origins, you can't use it with persons:
- Πάω στο Γιώργο "I go to George"
- Πάω στου Γιώργου "I go to George's (place)"
- ??Πάω από το Γιώργο "I go from George"
- Πάω από του Γιώργου "I go past George's"
- Περνάω το Γιώργο "I overtake George"
- ??Περνάω του Γιώργου "I pass through George's"
- Περνάω από του Γιώργου "I go past George's"
- Περνάω από το Γιώργο Not "I pass from George", but "I go past George's"
As for the purported illogicality of the expression—language is not formal logic: if it was, you wouldn't get defeasible implicatures (assumptions by your listener about what you mean, which may turn out to be wrong), and you wouldn't get the exploitation of defeasible implicatures (punchlines—you assumed I meant X, when I actually meant Y, so I momentarily tricked you in what I said). Defeasible implicatures is what makes language vivid.
And as we saw, the expression makes sense just fine, once you allow that people can both go to a place, and (then) from that place. Maybe you can't do that in Language Maven World; but Language Maven World is not a place you want to spend a lot of time in anyway.