Oh her parents are protective, but not too protective. That's a relief. But I can understand Nanami's anger. She lied pretty much because of her dad's way of being overbearing at times.
It probably makes her feel really bad being reminded of her troubles, and the fact that their relationship started with a lie. I sure do hope Youshin can somehow mitigate the troubles that are brewing right now.
Both Saya and Mom are happy that Nanami has a boyfriend. Mom especially likes that Nanami's happy when making the bentos. Dad is relieved that Youshin is a good guy, but I do think he's giving the wrong impression with his words.