People began using xz because mostly because they (e.g. distro maintainers like Debian) had started seeing 7z files floating around, thought they were cool, and so wanted a format that did what 7z did but was an open standard rather than being dictated by some company. xz was that format, so they leapt on it.
As it turns out, lzip had already been around for a year (though I'm not sure in what state of usability) before the xz project was started, but the people who created xz weren't looking for something that compressed better, they were looking for something that compressed better like 7z, and xz is that.
(Meanwhile, what 7z/xz is actually better at, AFAIK, is long-range identical-run deduplication; this is what makes it the tool of choice in the video-game archival community for making archives of every variation of a ROM file. Stick 100 slight variations of a 5MB file together into one .7z (or .tar.xz) file, and they'll compress down to roughly 1.2x the size of a single variant of the file.)