Their first argument was the term, "homosexuality" wasn't invented until the 1800s. However, these same people often claim the Bible was referring to pedophilia. But the term "pedophilia" wasn't invented until around the same time.
The purpose behind that was that the terms that were used before this point tend to sometimes be used to refer to both homosexuality and other things, and so when you read the terms you need to look at the broader context.
For example, the Leviticus verses. They almost seem like a clear cut condemnation of homosexuality, but that is only if you cut out 'מִשְׁכְּבֵ֣י אִשָּׁ֔ה' from the verse. The fact that that part is in there means there must be a broader context to the verse. The sentence is a clear and complete sentence without 'מִשְׁכְּבֵ֣י אִשָּׁ֔ה' and would be the clearest condemnation of homosexuality if written that way, and so one has to ask why it isn't written in that way. The conclusion, thus, is that 'מִשְׁכְּבֵ֣י אִשָּׁ֔ה' adds a context that makes it not a universal condemnation of homosexuality but a specific type of male-on-male relation.
The issue is that we simply don't know what it might mean. We can know it isn't talking about all homosexual relations but we do not know what the specific nuance is simply due to incomplete understanding of the language at the time Leviticus was written and there being no equivalent usage of 'מִשְׁכְּבֵ֣י אִשָּׁ֔ה' that would give us insight on what it could mean in these verses.
It is more important to read his work on the verses themselves as that is what he is going to grad school for than the intro.