In Ch. 217, Tenma told Harima that she would be competing against Harima Hario from here on. If Karasuma and Harima are coauthors using that same name, then to compete against "Harima Hario" means to compete against Harima and
Karasuma. This places Tenma in a double bind situation, where she has to choose between competing against "Harima Hario" and keeping her relationship with Karasuma intact. Harima wasn't bragging to Tenma - he was placing her into a situation where her goals conflict with each other. Expressed differently, he is saying "Which do you choose - the guy or the manga?" similar to how Eri posed a similar question in Ch.214.