His father is the sociologist and diplomat Martin Bútora and his grandfather from his mother side was the poet Laco Novomeský.

Bútora enrolled to study Library and Information Science at the Comenius University but did not graduate due to his focus on political activism and journalism.

Following his graduation, he started working for the Prague branch of Radio Free Europe and lead English language training courses for journalists.

He was also one of the founders of the Teach for Slovakia movement, which facilitates sending qualified teachers to schools located in the socially marginalized communities.

On 15 May 2023, the president Zuzana Čaputová assigned Bútora the Ministry of Education in her technocratic government under the leadership of the Prime Minister Ľudovít Ódor.