Why is 2-connectedness characterized by the existence of an ear decomposition ?
"Ear decomposition" is not a term I've heard before but it's incorrectly defined, as you've observed, since it doesn't require that the graph be connected, let-alone 2-connected.  An "ear" needs to be defined as having each endpoint adjacent to at least one further vertex of&nbsp;$G$.  (Actually, each endpoint would have to be adjacent to at least two further vertices, or the path wouldn't be maximal.)

With the correct definition, the theorem is true.