Threshold seems to be just a simple figure of speech.The threshold is the lowest part of the doorway, and if you are
big enough to get over it, you're in!

From the Internet:
Nonsense. “Threshold,” first recorded in A.D. 1000, descends from an Old English compound “threscold,” “doorsill, point of entry.” The “hold” has nothing to do with keeping one’s footing. The original meaning of “thresh” was “to tread, to trample.” Farmers originally threshed wheat, separated the grain from the chaff, by treading on piles of it. The treading seemed similar to wiping one’s feet at the doorway of a house, and that entrance took the name “threshold” from such threshing, or treading.