Since we're dealing with words... The word is its, in the context of its pedals! There should be no apostrophe, either in English English or in American English.
I think you can get a good intuitive feel for the forces on the wheel by imagining that you're riding the bike on layers of paper which can slide over each other if the tangential stress is above a certain value. If you're pedalling the bike hard and the paper starts to slip, it will slip backwards - visualise it or try it - because of the frictional force from the back tyre (tire). So the paper (or, without paper, the road surface) will exert a forward force on the tyre (Newton's Third Law). This is the force that accelerates the bike, or, if moving at a steady speed, balances the backwards force of air resistance on the bike.
But (you might argue) doesn't friction always oppose motion? Not exactly. It opposes relative motion between surfaces. The bottom of the back tyre is trying to slip backwards on the road, when you're pedalling. The frictional force on the bottom of the back tyre is therefore forwards.
When you're not pedalling there is a small backwards force from the road acting on the bottom of the tyre. To understand why, remember that there is a small frictional torque opposing the turning of the wheel. In order to keep the wheel turning as the bike descends the hill, there must be a small backwards force on the bottom of the back tyre.
Hope this helps.
