Magnetism and Current Contradiction

Hi I'm currently reading up on magnetism and its relation to currents but there's one thing that frustrates me and the textbook doesn't seem to elaborate on it.
 
I understand that a current produces its own magnetic field (and we use the right-hand rule to determine this), it also makes sense that if we throw a particle into this current-created field, we can measure the force it feels via F = qvB. What's frustrating me is that in the next section, the textbook outlines how if we place a current-carrying wire on a magnetic field, the wire will feel a force of F = i.l.b, but before it says that a current produces a magnetic field, so won't the magnetic field it produce partially cancel out the external magnetic field?

Thanks for your time.