This is just the way the physics engine works. You don't want to use physics for your character's control. Use the CharacterController instead.
An alternative (but messy) solution is to add a secondary/tertiary collider on the side of each platform and to make it frictionless. This can have unwanted side effects, extra work, and make you feel dirty.
My personal solution is to use Prime31's character controller for 2D, but if you are in 2.5D, I don't think this will work for you.
The reason this is happening is...well, I could make some assumptions, but that's all they would be. So I'll refrain. But imagine if you took a rubber ball and moved it up and towards a wall. It wouldn't just slide up. Anyways, the above solutions should work.