I don't think there's any point getting into another Limited vs Unlimited Atonement debate, so I'll just say quickly what Scripture and Tradition have to say on the matter:
St. John says: "he is the atoning sacrifice for our sins, and not for ours only but also for the sins of the whole world." The issue here is the use of the 2 phrase "not for ours only" and "sins of the whole world". This is diametrically opposed to the doctrine of limited atonement. It reminds me of the doctrine of sola fide where Calvinists interpret "not by faith alone" as "by faith alone", and "wills that all men be saved" as "doesn't will that all men be saved". (Kind of like the Catholic case: "A bishop should be the husband of one wife" interpretted "A bishop shouldn't be the husband of one wife" - but we don't believe in sola scriptura so we at least have a reason)
In any case, I think the whole thing is just another great example of the failure of the Reformation doctrine of the Perspicuity of Scripture. As Calvinists and Arminians prove by their continued existence, Scripture does need an interpreter, Moses' seat must be replaced with the chair of St. Peter.
The Patristic evidence is also in complete opposition to the doctrine, as the classic formulation was that Christ died for those whose nature he assumed, meaning all of humanity.
"Christ Jesus our Lord, as no man who is or has been or ever will be whose nature will not have been assumed in Him, so there is, has been, or will be no man, for whom He has not suffered- although not all will be saved by the mystery of His passion. But because all are not redeemed by the mystery of His passion, He does not regard the greatness and the fullness of the price, but He regards the part of the unfaithful ones and those not believing in faith those things which He has worked th rough love[ Gal. 5:6], because the drink of human safety, which has been prepared by our infirmity and by divine strength, has indeed in itself that it may be beneficial to all; but if it is not drunk, it does not heal." - Council of Quiercy 853 CE