Well let’s take your tooth example – here is what the regex-engine does (a lot simplified for better understanding)
Start with t then look ahead in the string – and fail the lookahead, as there is another t.
tooth
^ °
Next take o, look ahead in the string – and fail, as there is another o.
tooth
^°
Next take the second o, look ahead in the string – no other o present – match it, return it, work done.
tooth
^
So your regex doesn’t match the first unrepeated character, but the first one, that has no further repetitions towards the end of the string.