Q:

Why is it assumed that magnetic forces arising from magnetic fields do not do work on a current carrying conductor?

Imagine a long, thin current carrying conductor carrying a current $I$ and moving through space with a velocity $\mathbf v$. If there exists a magnetic field such that there is a force on the current carrying wire in a direction opposite to that of its velocity shouldn't the work done by the magnetic force on the current carrying conductor be non zero as the conductor is being displaced along the direction of its velocity? 

A:

Consider the well known "sliding rod in a magnetic field" setup:

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There is an electric current 'up' (electron current 'down') through the conductor that is moving to the right, and there is a force to the left acting to slow the conductor down.
The magnetic force on the mobile electrons, due to the motion of the conductor is downward while the magnetic force due to the electric current is leftward.

Note that the vector sum of these force components is always orthogonal the velocity vector of the mobile electrons, thus no work is done by this magnetic force on the mobile electrons.

However, due to this leftward force, the mobile electron density is greater on the trailing side of the moving conductor. The resulting electric field from right to left (within the moving conductor) produces a rightward electric force on the mobile electrons that just balances the leftward magnetic force.
But there is also a leftward electric force on the lattice ions on the leading side of the moving conductor with no balancing magnetic force.

It is this electric force that does work, not the magnetic force.

