If we change that age to 18 (as 16 is typically illegal here), even though I find the idea of huge age gaps icky, there's something about this stance that I instinctively dislike.
"My daughter is dating a 35 year old?!" is just a bit too close to "My daughter is dating a black man?!" and "My daughter is gay?!" It reeks of outrage born from disgust, rather than outrage born from genuine concern for the younger person's safety. It seems alarmingly... conservative in its psychological roots.
You just said that you think it's "icky". Maybe you didn't mean it. Maybe you just said it to slide in some pedantic BS to defend how you really feel. I don't know, but that's exactly how it looks.
I would have as much problem with a son dating somebody twice their age as a daughter doing that. If you're interested in learning a bit about the rational reasons people have for disliking middle aged men dating girls in their late teens, there's actually quite a lot of discussion about teenage mental development ever since this thread slid into the hell hole of pedo vs ephebo defending.