DisgruntledStudent's first two points are valid, because commercial anti-plagiarism scanners typically do retain anything scanned, and the fine print of their TOS often even includes clauses that actually transfer copyright ownership (or an unlimited-use license) to your work. However, the following three points are absolutely ridiculous:
3. It some cases, you may have included your personal information in the content and then you would not be able to remove it (either because you cannot prove you were the author or you have revoked your rights to your exclusive ownership).
Obviously, this is completely under the control of users, and any student trying to maintain anonymity would have to be an idiot to include personally-identifying info in anything scanned.
4. All plagiarism testing tools are unreliable. For example, they cannot distinguish between quoted text / references (you may include some quotes in your paper, which will be classified as plagiarism because the software doesn't know the difference between a quote and non-quote).
They're not perfect, but they're pretty good at finding overt plagiarism. Professors couldn't care less about properly referenced quotes that get flagged, incorrectly; but this is also completely under the control of users: smart users know to delete all quotes and the entire reference page before scanning, to get a more accurate result. Reference pages should be scanned separately, just to make sure the writer didn't reuse an entire list of sources from a previous project. Almost all sources will get flagged, simply because they've all been cited hundreds or thousands of times before; so, what you want to check is that your project doesn't contain a suspicious number of sources that appear together in some other essay or other work. Scanners also sometimes flag common word combinations, but anything flagged can be checked by the professor, because scanners also indicate where else the flagged content was found. No history or economics professor cares about any coincidental string of four or five words that also happened to appear in a completely different context in some Biology or Engineering essay that's totally unrelated to the topic of the history or economics essay. As I've explained previously, even within a history essay, there's probably no possible way to write that WWII began on September 1, 1939, when the Nazis invaded Poland in any combination of words that hasn't already been written countless times. Professors understand that, as well, and aren't concerned with those types of "matches" in any plagiarism scan.
5. If you are a student and submit your papers to Turnitin or other databases, you will not be able to use, either in full or in part, YOUR own papers for other projects or classes because they will be marked as "plagiarized."
This is even more ridiculous. Those scanners also record and display the original source of the flagged content, as well as the date and time that your essay was submitted for scanning. If your flagged content matches something published (or previously scanned into the system by another student at a different college) years ago, that's obviously a problem, provided the match itself is relevant and not just an unrelated coincidental string of words. However, if the only match of the content flagged is an entire essay first uploaded by someone at your college a few days before your deadline, it's obvious to your professor that it's only your own work that you scanned, yourself, in preparation for submission. That's particularly true nowadays, when many professors actually require students to submit their work to the student version of Turnitin or some other plagiarism scanner before submission.