In Nord society chickens are considered an important member of the community!
(But in fairness - take a kitchen knife and stab some random guy's dog to death. Don't be suprised if he starts hitting you - the idea of animals as someone friend or possessions really shouldn't suprise you...)
Killing someone's dog is different from killing their chicken, who they will be slaughtering themselves shortly.
@OP - Did you have your weapon drawn? If you killed this guy's chicken (which would look kind of insane) and then kept your weapon out as you walked around (and possible towards the guard), I can very well understand him attacking you. Or he was having a very bad day.
As for the guy who owned the chicken...he was probably just pissed.