I recently listened to James White's debate with Robert Sungenis on the assumption of Mary. It took place last Friday, and you can listen to it here.
White said most of what needed to be said. I don't have much to add, but I will make several points and recommend some resources.
Sungenis maintains that Mary's assumption is alluded to in scripture, but isn't directly or explicitly taught in scripture or by any extant extra-Biblical source in the earliest centuries of church history. He claims that the doctrine should be accepted anyway, largely on the basis of church authority. But he didn't produce much of an argument for that church authority during the debate. He claimed that some exercises of authority recorded in scripture, such as the rulings of the Jerusalem council mentioned in Acts 15, are examples of church authority. However, he didn't demonstrate that post-apostolic decisions should be assigned the same significance as decisions made by the apostles. And even if we were to assume the continuation of such an authority in post-apostolic times, he didn't demonstrate that the authority in question is to be found in Roman Catholicism. During White's cross examination, Sungenis said that we would be "up the creek" without such a post-apostolic authority. But he didn't demonstrate that having the Bible alone or some other authority structure different than that of Roman Catholicism would be unacceptable.
He also appealed to Marian apparitions. (See our thread on that subject here.) During White's cross examination, Sungenis claimed that Mary couldn't come back to earth bodily unless she had been bodily assumed to Heaven. But how does he know that Mary returned to earth bodily during the apparitions in question? And how would such a bodily appearance prove a bodily assumption in the first century A.D.? For example, some angels in the Old Testament era were given bodies while visiting earth without having been bodily assumed to Heaven earlier.
Sungenis suggests that some people believed in Mary's assumption or discussed it during the earliest centuries, even though they didn't leave any traces of those beliefs or discussions in the historical record. The possibility that such people existed doesn't give us reason to think their existence is probable. And see here and here regarding contexts in which an assumption of Mary could have been mentioned in the early centuries, but wasn't.
Sungenis also notes that people didn't know where Mary's grave was and were ignorant of other facts surrounding her death. He suggests that such ignorance has implications supporting Mary's assumption. But the early Christians were ignorant about the deaths and graves of other individuals as well, and we don't conclude that those individuals were bodily assumed to Heaven. See, for example, my quotes of Eusebius and John Chrysostom here.
Remember, Pope Pius XII, in his decree Munificentissimus Deus, refers to the assumption of Mary as "a matter of such great moment and of such importance" (11). He says to the individual who opposes the doctrine, "let him know that he has fallen away completely from the divine and Catholic Faith" (45). He claims that the arguments for the doctrine are so good that it "seems impossible" (38) to avoid the conclusion that Mary was bodily assumed. The Pope refers to the assumption as "this truth which is based on the Sacred Writings, which is thoroughly rooted in the minds of the faithful, which has been approved in ecclesiastical worship from the most remote times" (41).
Though the debate was about the assumption of Mary, Sungenis commented on other subjects along the way, like the canon of scripture. He said that the church decided on the canon in 382, but that the canon wasn't "formally dogmatized" until Trent. See here for a discussion of some of the problems with that argument. And since Sungenis raised the issue of how Evangelicals justify their canon, see here on that subject.