"Du" as well as "Sie" can be a sign of respect. "Sie" is very often used to reserve a certain form of distance. Offering "Du" shows, that a person in a higher position (teacher, coach etc) respects you as a person of equivalent rank. It is very common especially in sports for trainers and team mates to use "Du" even if the differences in age are significant (some of my old teammates actually had kids of my age themselfes). On the other hand if you don't feel comfortable beeing too close to someone (like a neighbour that you might like as a neighbour but don't actually want to invite over for a barbecue) using "Sie" is a polite but very obvious way to express this.
To me it was pretty unaccustomed that a lot of my professors and lecturers offered "Du" at the university while our teachers actually offered to use "Sie" when talking to us in the upper grades (some of them didn't really ask us if we felt more comfortable this way, they just used "Sie").
It really depends on the situation, I still feel weired when young people or kids use "Sie" because I still don't feel old enough to insist on this right, but I have to admit, that I feel slightly disrespected if shop employees or member of customers service use "Du" without a previous agreement.