Because she can use intuition, judgement, and wisdom to anticipate someone looking for her posts and maybe, just maybe save herself by getting to it before they see it. If you quote her text, you remove that option.
To be honest I personally don't see much of the point. I mean I get the logic is coming from, but it just doesn't really make sense to me. Because of the way the internet works it's literally impossible to prevent someone from finding out information about you short of becoming a hermit who lives in the middle of the wilderness. Even should you refuse to actually use the internet, we've reached the point of connectivity where it's totally possible to track someone purely through their interactions with people that
do, assuming you are patient enough. I personally can and have linked a person's potential real identity to them, even with them taking basic precautions, just to prove to them that it could be done if you were willing to be patient enough. (Of course it's not like I announced it to the world or anything, they just wanted to know if I could do it). In this case you could probably reconstruct a fairly valid profile just by going back through the posts and looking at the responses to them, as well as the last times they were edited. If any were edited recently that means they were probably more likely to contain things you would be against. (Heck, if you were really thorough you would be able to pull up this discussion and much more definitely link recent editings to things that you would disagree with!)
Once you assume that people
can find out whatever they want about you, regardless of what you do, it becomes a simple effectiveness vs. cost curve, where you can rate how effective methods are at slowing down people who want to find out about you against how much it costs you and other's to do it. Asking people to not quote you is like,
way down on that curve, and there's tons of things you should be doing before that to maximize your protection. Simple things like using different usernames on different places, not posting multiple details about your life in the same place, tweaking slight details in the things you do post, and running through proxy systems or even hardcore anonymizers like tor.
Assuming you are doing all of those things, asking people to not quote you on the off-chance you can change it without someone putting it back together it is like hiding under your blanket in you locked bedroom inside your moat-ringed castle on the off-chance that any attackers won't be able to find you under it (after they have already swam the moat, breached the walls, and battered down your locked door). Sure, it adds a minuscule bit more of protection, but it certainly inconveniences the others in the room who are trying to talk to you way more than any form of additional protection it provides.