Settlers of Catan: Building Roads 'Through' Settlements
The reason it is no, is because when you build something new (except for the set up rounds) you need to build roads and settlements connected to something you have already built.

When you reach someone else's settlement with a road, it 'fills' up the intersection and by building a road past you would be trying to build onto their settlement not your road.  It works the other way too, if you have a long road and someone build a road to an open intersection on your road they can build a settlement on the end of their road and thus split your road into two.  So this is a reason not to go crazy building roads without settlements.