About "προβαίνω τῶν θυρῶν"

Is the τῶν θυρῶν a separative genitive? I guess it means “I get out (from the door)”. But it seems a little strange. (maybe just a language habit?)

προβαίνω τῶν θυρῶν sounds like complete nonsense to me.

yeah, I think so, too.
It comes from Daphnis and chloe, and the original sentence is “Οὔτε οὖν ἀγέλην τις εἰς νομὴν ἦγεν οὔτε αὐτὸς προέβαινε τῶν θυρῶν, ἀλλ’ οἱ μὲν λίνον ἔστρεφον, οἱ δὲ πάγας ὀρνίθων ἐσοφίζοντο.”

TLG gives αὐτὸς προῄει (not προέβαινε) τῶν θυρῶν.
The Bailly dictionary, under πρόειμι (2), gives the following explanation: 2 se produire en avant ou au dehors, sortir : ἔξω τῆς φάλαγγος, XÉN. Lac. 12, 3, sortir du rang, litt. de la troupe ; τοῦ οἴκου, HDN 1, 17, sortir de la maison.
I think it just means “to get out of the doors”.
Hope this helps.

yeah
I guess it may just be a kind of habit or usage

It’s true that Longus doesn’t use προβαίνω, but there’s nothing nonsensical about προβαίνω τῶν θυρῶν. I imagine whoever produced Vicoland’s text changed προῄει to προέβαινε to make it easier for beginners. εἶμι is a verb that often causes difficulties.

It’s obvious that a modern speaker changed πρόειμι to προβαίνω. But a comparison of the LSJ entries for the two words will show that far from being drop-in equivalents, they are used fairly differently, with πρόειμι regularly taking the genitive, and προβαίνω not. And the “go forth + gen.” usage isn’t indicated for for προβαίνω.