In fact from childhood Logan's role model was his elder brother Enzo. He admired everything about his brother and thrived hard to be like him. Even though Enzo was cold and aloof to others he showed his soft side to Logan and occasionally pampered him.
In school no kid dared to bully Logan after knowing he was Enzo's sibling, Logan became proud and boasted to everyone how powerful his brother is.
Whenever Logan did any mischief his brother saved him from elder's wrath but later punished him to teach a lesson. Logan was quite possessive of his brother and did not like sharing him with others.
Before Enzo had no girlfriends and this made Logan spoiled and little bit arrogant. But now that Enzo was dating Hazel, Logan felt someone has taken his spot and his brother no longer cared for him.