In a way she's right. In a sane or sensible world, we should be conservative, pack our own lunches and not dine out as much or eat at fast food restaurants. We spend hundreds of dollars each year on McDonalds. So from a conservative point of view, it's too much money for a set of headphones.
That said, if you classify it as a high end hobby, high dollar is normal. Look at people who spend money on their Harley Davidson motor bikes. And those bikes won't last more than 20 years if riding on them all the time maybe. On the flip side of the argument, a good set of headphones will last at least a generation or longer. I bought a set of AKG headphones for a few hundred dollars and they will give me sonic bliss for a long time. Arguably, it's high quality with longevity. In that regard, it's worth it.
However, if one keeps buying expensive headphones every year, that may be economically foolish. I'm done with headphones and pretty much halted my headphone hobby and expect my headphones to last many years, so for me, it's money well spent.