No, everyone wants to see a mutual understanding of each other.
Sympathy or the art of hoarding sympathy is a Narcissistic Personality Trait.
How amazing is this book?
http://www.etymonline.com/index.php?term=mutual
mutual (adj.) Look up mutual at Dictionary.com
late 15c., originally of feelings, from Middle French mutuel (14c.), from Latin mutuus "reciprocal, done in exchange," from PIE root *mei- (1) "to change, exchange" (see mutable).
That is common which pertains equally to two or more persons or things.
That is mutual which is freely interchanged: mutual love, affection, hatred. The word is sometimes incorrectly used for common: our mutual friend, a phrase of very frequent occurrence, no doubt owing to the perfectly correct 'mutual friendship.'
[J.H.A. Günther, "English Synonyms Explained & Illustrated," Groningen, 1904]
Mutual Admiration Society (1851) seems to have been coined by Thoreau. Mutual fund is recorded from 1950. The Cold War's mutual assured destruction attested from 1966. (Assured destruction was an early 1960s term in U.S. military policy circles in reference to nuclear weapons as a deterrent, popularized c. 1964 by Robert McNamara, U.S. Secretary of Defense under Lyndon Johnson, e.g. statement before House Armed Services Committee, Feb. 18, 1965; the mutual perhaps first added by Donald Brennan, conservative defense analyst and a public critic of the policy, who also noted the acronym MAD.)
Translation, everyone want to be under and standing under (supporting) each others love.
I could be wrong, as they are fairly similar.
http://www.etymonline.com/index.php?allowed_in_frame=0&search=sympathy&searchmode=none
sympathy (n.)
1570s, "affinity between certain things," from Middle French sympathie (16c.) and directly from Late Latin sympathia "community of feeling, sympathy," from Greek sympatheia "fellow-feeling, community of feeling," from sympathes "having a fellow feeling, affected by like feelings," from assimilated form of syn- "together" (see syn-) + pathos "feeling" (see pathos).
In English, almost a magical notion at first; used in reference to medicines that heal wounds when applied to a cloth stained with blood from the wound. Meaning "conformity of feelings" is from 1590s; sense of "fellow feeling, compassion" is first attested c. 1600. An Old English loan-translation of sympathy was efensargung.