In proper Mandarin pronunciation, "Xi" sounds more like the second syllable of "missy" not "she".
And to me, Mandarin 'xi' sounds a lot more like "she" than "see".
On the other hand, I'm a Southerner, so I don't usually distinguish between "sh" and "s" sounds. I can do the 卷舌 thing, though, well enough that Northerners tell me I'm doing it right, and I don't think either Pinyin "shi" or Pinyin "si" sound anything like English "she". And while I don't think Pinyin "xi" sounds exactly like English "she", I think it sounds pretty close.
This is an issue lost on most native speakers of mandarin, and it’s hard as hell to teach to learners.
pinyin —> proper sound —-> actual sound
xi —> she —> see
si —> suh —> suh
shi —> shuh —> suh
chi —> chuh —> tsuh
ci —> tsuh —> tsuh
There are more, but I’m too many beers in now to remember.
The best test is to ask someone how to say 四十四是四十四 (44 is 44). It’s a good test for tones. This is properly something like /shuh suh shuh shuh shuh suh shuh/. In vernacular, this usually becomes something like /suh suh suh suh suh suh suh/ with tones being the only hint at different words.
Chinese is fun.
I forget the details now, but “standard” putonghua has two variants, and each variant revolves around Jiangsu province (something like north and south?). Anyway, Beijing people think that they speak the “standard”. People educated in linguistics know better.