Let me be the advocate for my brethren who dislike her. Why is she annoying? First of all she seems to be a lesbian currently it's already a great turn off, at the very least because she hides it, she doesn't try to confess to her love in order to resolve the tension and lastly she made up an ambiguous reason to shot down MC.
Let's be honest, if she told him in secret: Sorry, I like girls, i consider you a fine friend but nothing more. This would resolve all the problems. First of all our MC would move on and do more productive things in his life than to pursue a dead end and waste energy and emotions. Secondly she would eventually resolve her own issues and move on from mangaka IF she is not bi or lesbian.
To this point her actions seem to reek of cowardice and deception not to mention her stone faced expressions and being a stick in Glasses-kuns and mangakas progressions (she pops out to destroy the dynamic). Let's be honest, cowardice is objectively unattractive point in any person.
Also let me mention this, she didn't set up unreal reason for rejection, MC literally can improve his drawing skills and then he will confess once more only to meet another idiotic explanation? Let's delve deeper, was our MC's objective in life to become a mangaka? Is it his future career plan? Currently it seems he is only doing this for her, so if his love interest doesn't answer him after he learned and wasted his energy on useless endeavour, how devastated he would be? Those questions that i made right now would pop-out in any empathetic good person, she on the other hand lacks those traits which makes her the opposite. She didn't consider that she just ordered him to go on a wild goose chase.