When you deploy flaps, you will almost always induce a nose-down pitching moment for the WING. As a pilot, you don't care (and really can't tell) if you induce a nose-down pitching moment for the wing. What you care about (and what you can see) is whether flap deployment induces a nose-down (or nose-up) pitching moment for the AIRCRAFT.

If the induced pitching moment for the wing is almost always nose-down, how can the induced pitching moment for the aircraft be nose-up? In most instances where this is the case, flap deployment creates a downward component to the air approaching the elevator/horizontal stabilizer/stabilator. This causes the elevator/horizontal stabilizer/stabilator to push down more (or possibly push up less) and the NET result can be an AIRCRAFT that wants to pitch up with flap deployment. For certain geometries (like T-Tails) flap deployment tends to have little influence on the flow over the tail and the effect of flap deployment is typically nose-down. For other geometries (like a T-38 with closely spaced flaps and stabilator) the effect can be strongly nose-up. So you can look at the gemerty of an aircraft and predict what you might see, but it's possible for the aircraft to pitch either direction with flap deflection.