Smash. You can sit there and play semantic word games all day long, and it will never change the fact that the very fact that unions can strike to force their employers to pay them more and/or provide them better benefits means that they have a monopoly.
Period. If they didn't, strikes wouldn't work. Anywhere that a strike doesn't provide a benefit to workers, the union isn't a monopoly. But then it's also useless, isn't it? Anywhere that they can strike and get a better deal, by definition they are a monopoly.
It's just not that complex. Unions are monopolies of labor. Always have been. Everyone understands that they are, but have looked the other way because they believe that the good to workers outweighs the fundamental unfairness that labor unions represent.
I could get you making the argument on the issue of labor being important enough to make an exception. But arguing that unions aren't monopolies? That's weak...