He was a kid
Seeking revenge is the natural instinct to what he's been through. Finding out his brother's truth hit even harder, seeking revenge is also the natural instinct. The world betrayed his brother. Sasuke had it much worse than Naruto and Itachi.
Tobirama gave a detailed explanation about the uchiha, their sharingan powers grow stronger the bigger the heartbreak is, they're people who love their family deeply.