Question: In the usual aircraft configuration, the center of lift is located behind the CG producing negative pitch moment (the horizontal stabilizer counteracts it by producing downforce - positive pitching moment). If the aircraft rolls to one side the vertical component of lift on the wings would decrease, so by that logic the aircraft should pitch up.

Why does it pitch down? What am I missing?

Answer: 
The answer is that the aircraft doesn't actually *pitch down*. When banking (or rolling) into a turn, the angle of attack (or the angle between the center of the wing and the flight path of the aircraft) stays the same. Assuming no correction to maintain altitude is made, the aircraft will continue on the same angle of attack, just banked over by some amount. Due to the bank, the lift produced by the wing is no longer vertical, instead, it is directly perpendicular (at least for our purposes) to the wings. Therefore, if the airplane is in a 30 degree bank, then the lift vector will also be 30 degrees from vertical. Doing some vector analysis, then you can determine that if the angle of attack hasn't changed the new *vertical* component of lift will be about 86% of what it was in level flight. Therefore, the plane would begin losing altitude. This altitude loss is what you see as the airplane pitching down.
Darjan, first the basics. An aircraft in straight and level flight has the center of all lifts balanced with the center of gravity. A plane with the center of gravity set forward of the WING center of lift requires down force on the tail to balance it.

Now roll 45 degrees. Gravity vector is no longer aligned with elevator trim. If you roll 90 degrees the rudder is now you "elevator" relative to CG. Unless you apply opposite rudder, a
forward CG set nose will drop. This, among other reasons, is why aerobatic planes like their
CG further back.

Agree with @PilotDan that bank will also cause reduced vertical lift, but a forward set CG will also drop the nose. Many pilots will try to pull harder on the yoke to maintain altitude, adding power seemed to work better for steep turns, as well as reducing bank angle.

Bottom line, forward set CG is not a panacea of safety in all cases. Published forward CG
limit is best adhered too.