I think that quote is some kind of hint as to the nature of the plot. My hope based on the very last line would be that Byleth betrays the three lords and turns to the other side, resulting in a much darker story. Even when he’s the enemy Edelgard still feels a bond with him and doesn’t want to lose that. But when taking into consideration the context, I don’t think it’s very likely. If I were to place a bet it would be a generic time skip like most people are suggesting.
However generic time skips are, well, generic, so I’ll dive a little deeper. Now there is a plausible scenario that fits the last two lines very well, especially if we consider Edelgard’s prior rant about the crests. Since she’s lecturing Byleth/the teacher about them, it would be reasonable to assume that he is either unfamiliar with them (hailing from another land), or holds the opposite opinion as her. In either circumstance, should Edelgard decide to start a holy war, she wouldn’t assume Byleth would stand alongside her, as he would either side with the church for the crests, or have no stance on the matter. Therefore it seems quite possible that Edelgard abandons his tutelage, and her fellow lordlings, in pursuit of a way to destroy the crests.
Hopefully we get some more info today :)