I think the mostly likely reason we don't see evidence for intelligent life in the universe is simply because we don't realize how unlikely it is to evolve intelligence.

Maybe there are a lot more evolutionary paths life can take on a world than just something similar to what happened here on Earth. Maybe typically it's unlikely for life to evolve to become much more than plant-like life forms.

I'm sure there are species in the universe which have evolved intelligence but I think they're much rarer than we would assume here on our perfect example world, Earth.