If that last sentence seems a little confusing (if you're still in the act of buying something, why would you be wondering already how you can care more about it?), Cline clarifies by giving the example of a clothing item she bought inexpensively that soon needed a repair. She might have junked it, since it didn't cost her much to start with, but she decided to mend it anyway, and then found she really liked it.
How useful or true is that idea? While I have, not infrequently, re-donated thrifted items after a very short ownership (clothes didn't fit, hated the book after one chapter, or realized I already had a copy), I do generally try to take as good care of inexpensive/thrifted clothes as I do of more expensive ones. Like washing them on Gentle and line-drying them, instead of ruining them in the dryer.
I don't think that really solves the problem of whether or not you should buy inexpensively-made new things (although that's a lot of what Cline's book is about); but it is a good way to perhaps look differently at those you already have, wherever they came from, or however much or little they cost.