Spiders can see you through the door and other blocks when they are not supposed to.

I remember the bug in 0.6.0 that creepers can blow up if they see you through the door. This bug is the same with spiders, they can see us through doors.
note: Its supossed that spiders follows you around solid blocks if you see them, but either if you dont see them it will be following you around your house(here the problem).