Pretty sure it was a mix-up with the translation at the beginning. Eirin had always thought she was a lizard, one of the lowest species. The Etam family worships dragons, but doesn't like lizards which is why she was kicked out in the original story. If she was a dragon, her exile wouldn't make sense in the original story.
The etam family has the blood of the dragon hence the main line's excessive mana and abnormal physical strength. Eirin's "parents" as she knows is from a really distant collateral line so the chance of inheriting dragon blood is thin as a thread so she doesnt think shes a dragon at all.
Plus her animal form is similar to a lizard so its not unreasonable she thinks that way. Tbf itll take time before we get to the confirmation if shes a dragon or not(which spoiler: she obv is)
Didnt you say you were a dragon at the start????
I thought FL already knew :/