To make it simple it is important to bear in mind that Chinese has one more extra vowel that most Indo European languages lack
The ï - an i with the 2 dots on it, a “centralised” i. In the Wades Giles system this is the “-ih”.
This “ï” is found only 6 times in today’s Chinese language - with consonants (in Hanyu Pinyin) s, sh, c, ch, z, zh to form the phonemes si, shi, ci, chi, zi, zhi.
Unfortunately, there are also 3 phonemes beginning with s, c, z and ending with a normal “i” - the “i” as in “mint”.
There cannot be 2 pronounciations to the same spelling, can there? So the folks behind the entire pinyin project probably decided to combine the phonemes with the normal “i” with x, q and j, giving rise to Xi (pronounced as “See”), qi (“tsee”) and ji, while instructing everyone else to read “si”, “ci” et al as /sï /, /tsï /, to avoid confusion and the introduction of a new letter.