Regarding the on'yomi shi (シ), of the character 思 from the word 思う, why does Google Translate list the pronunciation of this word/kanji as shitau instead of shi (with shitau missing from the dictionary entry as displayed below in Takoboto):
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To answer your specific question, of " why does Google Translate..." -- it is a machine program, and thus it is only as good as the data fed into it, combined with the cleverness of its algorithms. Clearly, the programmers have not finished programming Google Translate to correctly handle Japanese.
In short: Never trust Google Translate. Especially when it comes to single words. The reading shitau is for the spelling 慕う, and it means "to yearn for, to long for". 思 on its own is read (generally) as shi and is only used this way in compounds with other kanji.