It is not a contradiction at all. Some unskilled labor positions (especially ones that are seasonal in nature), will go unfilled, without those immigrant workers.
That's easy to say, and impossible to prove without a deeper analysis, which would be incredibly hard for you since the workers you are defending are *undocumented*. And since your point hinges on unemployment numbers, you'll need to present a detailed analysis on how many illegal/undocumented workers are in the workforce, as well as a detailed breakdown of the unemployment numbers--which do not include those who have been unable to find employment
and have given up looking for work.
IOW, there are an unknown number of illegal workers, and an unknown number of people who are unemployed and not accounted in the stats you present, yet you claim that OTHER people are oversimplifying the issue.
But at the same time, the model of employment markets works on the principle of supply/demand, so it's by definition that adding workers to the market will almost certainly lower wages.
So, you can either bring us details to support your argument, or you can just walk away at an impasse. And even if you support your "they wouldn't want to work those jobs anyway" argument, you'll still need to explain why undocumented foreign workers is the answer, as opposed to documented, legally imported workers.
Edited to add: It'll also be hard for you to simultaneously refer to them as "undocumented", as well as their lacking a criminal record. The concept of "undocumented" means that we don't know their background. IOW, we don't know who we've let in, thus which of them have histories of violence, etc... thus which of them are not the ones we want here filling these jobs. This plays into the point you're yet to respond to--even if we need imported workers, why are unlimited, undocumented workers the answer as opposed to limited, vetted, and documented workers?
