Of all the Hoshidan royalty, Takumi is by far the most emotional, to the extent that when Corrin is rescued and brought back home, he's immediately suspicious and treates Corrin with hositility. This is because Takumi, despite being a crown prince, seeks to get recognition for his abilities. He feels overshadowed by Ryoma, and thus has worked tirelessly to prove he can be as, or even better, than his siblings.
This also shows when he deals with the people of Nohr, who he at first believes is beneath him, often calling them scum of the earth. His emotions also lead to his suspicious nature, often seeing trouble where they often isn't any.
Despite this, Takumi can overcome his prejudices and become a better preson. Or, if you don't choose Hoshido, he can become the greatest enemy you will ever face. The choice is yours.