Under the ToS of all plagiarism detection software (at least that I've looked at), the student's work is added to the corpus against which all texts are tested against. This is what you would _obviously_ do if you were building a plagiarism detection app, however that means a student is forced to submit work to a private company, which will then profit off of their work.
You might say what the value of a gen ed term paper is to a student, and I'll agree it's not much. But that's not the point. The student is forced to provide that to a third party by the school, which will then profit from it. This isn't a Facebook-like situation where you can just not make a Facebook account. I would guess in many schools, refusing to submit to plagiarism detection software would be taken as evidence of plagiarism.
This is probably a few years out of date, and I see that Turnitin recently shut off their 'upload your own work so you can see if it's plagiarized' product, but for a student to have an active defense against plagiarism _costs money_. Yes, if a student wanted to make sure their paper wasn't accidentally plagiarized (this is common, because their algorithms are shit), that will cost a few dollars. This is unacceptable.
And for anyone who says, 'just transfer sections to a prof that doesn't use the software', there are contracts with entire departments and schools, which then force professors to use the software. Yeah, you could transfer _schools_, but the point stands.
Plagiarism detection software -- which purports to support the intellectual property of the author -- does just the opposite.
Also, I should mention that if someone wanted to cheat, they wouldn't plagiarize; they would simply get someone to write a paper for them. This service is far, far more common that you would believe.