Everyone with an iPhone tells me they can see when I'm texting back because of the three dots. My question is: why can't I see the three dots when someone is texting me? I have an iPhone SE.
The 3 dots only show when someone is using iMessage. If someone is texting you via SMS you won't see the typing awareness indicator.
It is possible your contact has a jailbroken phone and has disabled the typing awareness indicator. The indicator also will not display if they receive the text but, for some reason, lose internet connectivity while they are writing their response.
If that person is replying and not using iMessage (eg. if they have it disabled, or temporarily disabled) then the indicator will not appear either.