The dad actually deeply loves and cares for her but his communication skills are literally maxxed zero and his emotions on his face are negative, the reason, he is also "cold" is the emperor keeps the dad on a leash by constantly threatening his only daughter, it's going to be quite a long time before we see it in the webtoon but both of them misunderstand each other a LOT and I do mean a lot, the dagger scene for example, the Dad, actually handed her the dagger to protect herself if, someone tries to attack her, he thought she'd understand overestimating their relationship, the only reason, he's even putting up with the royal family is to ensure her safety because most of the family members are complete scum, except the 2 which I won't spoil but there you go, spoilers from novelupdates btw lol