“Is this tree healthy?”
To answer this question, we have to ask ourselves, “what is tree health?”
From an arboriculture standpoint, tree health is separate from structural integrity.
Tree health means that the tree is free of pests and disease, is vibrant and vigorous, showing appropriate new growth for its species each year, and has adequate bright foliage and blossoms.
Structural integrity refers more specifically to the tree’s form and structure.
Occasionally, due to pruning or growing conditions, a perfectly healthy tree may have structural defects or problems (e.g. broken branches or stems, cavities/wounds, or congested crossing branches in young trees). Other times, structural defects can be caused by, or result in, the introduction of pests and disease.
As you can imagine, an arborist will be looking at both the health and the structural integrity of the tree.
As a property owner, these two distinct but related concepts can become blurred in the question of whether or not the tree is healthy. Furthermore, your concerns about the health of a tree may also be coming from a safety concern, and the confusing part is that an unhealthy tree may not pose a safety hazard while a perfectly healthy, structurally unsound tree could be quite dangerous.