You are talking about the time you leave the office and the time that your friend leaves the office, and are wondering why these two times match: note the plural. As an affirmative statement, you would therefore say
Our times always match.
When you make a question, you have to invert the subject and the auxiliary verb. If there is no auxiliary word, you add do as an auxiliary verb, then invert it.
Our times do always match - add do as an auxiliary verb
Why do our times always match? - invert subject and auxiliary
The correct sentence is therefore
Why do our times always match?