The oldest child may feel slighted by the parents in favor of the youngest child. The youngest is often a quite skilled and adept manipulator. He/she is the one who often harasses the oldest child and when the latter defend himself/herself, the former cries foul, citing bullying. Of course, the parents will be on the side of the youngest child because he/she is "the baby", "the innocent" and " do not know any better."
Also many oldest children are treated the most harshly by the parent. They are also discarded by the parent in favor of the youngest child. Of course, the oldest children will feel resentment towards this youngest child and will take out his/her angst and/or frustration on the youngest child, that is only human nature. In addition to that, youngest children are oftentimes the parents' favorite and receive the most preferential of treatment while oldest children receive the most differential treatment. Of course, this parental favoritism is bound to cause further resentment, even hatred on the part of the oldest child towards the youngest child. Many favorite children are often bullied by the less favored children in the family as a result of such unfair parental treatment.
Then there are oldest children who believe that because they are the oldest, they have the power to treat the youngest sibling as they please. They believe that since they are the oldest, might=power=right. They see their power as pure power and carte blanche to exercise their liberties towards the youngest child.
In order to not to foster bullying and/or otherwise aggressive behavior on the part of the oldest child towards the youngest child, treat ALL children fairly. Realize that the oldest child is still a child. Do not expect him/her to be always be the perfect and stoic one. Oldest children deserve a normative childhood and adolescence also. Do not overburden the oldest child with so much responsibilities that he/she does not have a normative childhood.
As far as the youngest child goes, do not coddle and baby him/her. Also give him/her responsibilities at the same age that the oldest child start receiving responsibilities. If the youngest child does something wrong, punish him/her as you would the oldest child. Do not treat him/her preferentially over the oldest child. Administer discipline to him/her as you would the oldest child. Also, do not forget to regularly hug the oldest child.