It is an issue because they're nobles of some standing (and this is a manga from Japan, the country of absolutely labyrinthine levels of politeness and social etiquette all based around being extremely deferential and non-confrontational). There's a whole giant song and dance of rules and etiquette that they'd have to follow and her just coming out right at the beginning and saying "No. Go away." would be seen as incredibly rude and improper.
Chances are if the MC doesn't intervene and cause things to spiral a bit out of control what would end up happening is that she gets to the end of their time together, possibly after the tour she's taking him on, and then she lays out her reasons for not wanting to marry him.
Yes it's a manga from Japan,.. but it's not playing in japan, nor is it following the actual society of japan, also didn't say she's supposed to be rude to him, i only said it's unlikely to cause problems, if she voiced her -opinion- to him it's not their parents or anyone is present
Also she has yet to suggest, or say to anyone (for the reader only even) that she has feelings for Yuuki at this point, though the romance tag suggests as much, maybe we get a twist 😶