Quick context: I was reading about a Greek word in the bible that always means " generation ", but is twisted by some people into meaning " race ". Below is a scholar with his say on the matter.
" (Genea) has been taken to mean The Jewish Race, or Unbelieving Judaism. It is unlikely that such an improbable meaning for the noun would have been suggested at all without the constraint of apologetic embarrassment…! "
Why does he say without instead of with? What he is really trying to say is - apparently - this : with the constraint of being embarrassed, no one would make such an assertion ( that the greek word means " race " ). Or, alternatively : " without the constraint of embarrassment, anyone would have the audacity to make such an assertion."
If the author had dropped the word " constraint ", his sentence would have made sense and not been awkward.
something like this would have been fine : it is unlikely that such an interpretation would have been suggested without embarrassment.
thoughts??
I have a different take on the sentence than what you say it means.
I think “It is unlikely … without the constraint of apologetic embarrassment” means “It was made … in the constraint of apologetic embarrassment”. In other words, those who ascribe the improbable meaning are doing so because they are embarrassed and apologetic (because what Jesus said did not come to pass, looking at it from the perspective of present day) - I checked the page the sentence was cited from 
“Jesus was wrong” coming right after the quoted sentence is a strong clue for this.
I suppose you took the “apologetic embarrassment” as a general reaction of people when making a transgression (of ascribing improbable meaning to “genia” for example"). What he was getting at, I believe, was the sentiments of those who actually made the suggestion. He is saying they are apologetic because Jesus was wrong, and if they weren’t, they wouldn’t make such improbable suggestions.
So I think “without” is indeed correct in the sentence.
I see. So the author is saying : " because they are ( already ) apologetically embarrassed, they are making that suggestion. "
" without (already) being embarrassed, such a suggestion wouldn’t have been made. "
Tough one.