I'm not quite sure what you mean here, in part because of the tense change from "why did the church embrace" to "Isaiah is not correctly cited".
I suspect that the author of gMt (a Greek text probably written circa 80 CE) was informed by the LXX and looked to it for prooftext. I see no evidence to suggest that it was obvious to the author or his milieu that there was anything problematic about the Greek rendering of the Hebrew almah.
Assuming the author looks to it as a proof text then I'd expect him to be looking for proof of something, but it seems he isn't. That undermines an assumption. The problem for this assumption is Matthew's inclusion of the term 'Fulfill'. Here is an article which cites all twelve of his uses and the three approaches to determining what he means by it.
Matthew's Use of the Term "Fulfilled"
Lets go with approach #1 from the article: "
Predictive prophecy never existed, hence the apostolic claims of such must be dismissed." If true Matthew cannot intend that Jesus mother is a virgin merely because of a prediction in Isaiah. There is no prediction, and he knows this and therefore ignores, completely, the state of the woman in Isaiah. Instead he implies Jesus birth is
good omen like the birth of that boy in Isaiah. In this case its likely long after that fact of the writing than anyone misreads Matthew's intentions to be using Isaiah as a proof text related to virginity.
To summarize: the origins of the church being both obscure and widely misunderstood and speculated upon by scholars of many stripes, there is no reason to make the assumption that Matthew is searching for a proof of any anyone's virginity. He may be alluding to Jesus birth as an omen of good fortune.
***edit*** changing the word 'Omen'. It doesn't fit what I'm saying, because omens may imply prognostication.