Both parents don't necessarily have to stutter (both my parents do not, but people in their family do, especially on my mum's side). I'll bet in my case, the "trait" is prevalent in both my parent's gene pool, and just happened to manifest in me (sadly). For example, my mother has 2 siblings who stutter (my aunt and uncle), and one of her nephews (my cousin) from another of her non-stuttering sibling (another aunt) also stutters. I can barely recall anyone on my dad's side who stutters (though i'll bet there are), but it's obviously it's stronger on my mum's side.