As you said, respect should be mutual; But, it is unnecessary to respect anyone just because he or she is older than you. Particularly in India and some Asian countries, there is a tradition of respecting elders even when you salute them (we are not allowed to call their name also, if you do; that is a lack of respect!).
'"Everybody should respect elders" - a quote by elders' is a joke that we share often.
RE: Respect To All