Sibling rivalry has existed since time immemorial.  If you have a family with multiple children, you have sibling rivalries - they are an unavoidable fact.  The term "sibling" of course refers to children that are related and who live in the same family.  Parents often find it difficult to handle sibling rivalries.  It is one of those issues that is difficult to tackle equitably and fairly - from the perspective of the child.  Children are sensitive and have a tendency to hold grudges (sometimes for a long time) if their parents are not seen to have been fair in dealing with them and their sibling(s).  As a parent, of course, you try to be fair and impartial towards all your children.  However, as parents, you never can truly be impartial to all of them.  You almost always have certain views (real or imagined) about your various children and tend to resolve conflicts between them based on those views.  That's never a good idea and can build resentment in the affected child.  For example, if you feel that a certain child is by nature a well-behaved child (in your view) - you would tend to favor that particular child in a conflict situation and tend to admonish the other child (that in your view may have a tendency to initiate conflicts).

So, as a rule, you should never let your preconceived notions about your various children influence you when you are dealing with differences/conflicts between them and trying to resolve them.  Whenever a problem arises between your children, always deal with that problem with the given facts of the case then and there (not from your past experiences).

Parents also make the mistake of comparing their children and discussing those comparisons with the children themselves - big mistake!!!  Of course, the child that is praised feels good about the praise, but what about the child that is criticized or spoken negative about?  Parents never think about how that child would feel and what possible good can come about by telling that child that they are not good enough vis-a-vis the other one!  It just puts that child down and makes that child feel less loved.  Each child has his/her own personality and traits - celebrate that fact and judge them for what they are, and not what they should be vis-a-vis someone else or what you expect them to be.  A child, for example, may not be as academically gifted as their sibling(s), but does that mean they are any less or should be loved any less or made to feel bad about that fact?

The order in which you are born also tends to create problems, generally because parents don't realize the potential for those problems and don't know what to do to deal with those potential problem situations.  For example, you would often see parents putting undue pressure on the eldest child while doting on the youngest one.  The middle child often feels left out.  They don't know where they fit in and what their role is or should be.  Parents also tend to exacerbate this feeling by focusing more on their eldest and younger child, without meaning to do so of course.

The key to dealing with sibling rivalries therefore is to look at each individual child for what they are and dealing with them individually on that basis.  While dealing with them in a group, make sure you aren't putting one of them down by comparing them to the others.  Don't rush into making pronouncements of guilt or blame.  Take a time-out and evaluate the situation and then talk to them fairly and equitably.  Let it be made known to them that you are a fair parent and you love all of them equally!!  Most parents would argue that they are fair to their childen; of course, they are --- but its equally important to try to appear to be fair in their eyes as well.