Not every kid who learn an instrument come from a family of musicians. Some discovered they have an interest in piano, violin or whatever at a young age. Their parents recognize their interest in music and start lessons soon after.
Coming from a non-musical family, my parents were open to kids taking music lessons. But they have little interest in music besides listening to the radio. Me and my siblings had taken lessons at a young age. My parents weren't supportive besides telling us that the teacher always sounded better and we don't practice enough. Without positive feedback,we resisted music practice and eventually quit.
Of course many people like myself stopped playing for a while and eventually resumed as an adult. People from musical families have the advantage of getting problems resolved with other family members. There is also the advantage of family members playing together as duet or trio sort of thing. Some parents push kids into music lessons and practice which can damage a child's self-esteem.