Based on the comments and with help from ChrisW it was determined that the points were unavailable to participate in the Network because they were of geometry type multipoint (multiple points for a single row):
A Multipoint geometry represents an unordered collection of single
locations in space, and can be used to represent geographical features
which have multiple single locations but which represent a single
geographical feature, for example the multiple entrances to a single
Which cannot participate in a network, according to the help document for creating a geometric network:
Only point and line feature classes are supported as input. The
feature classes cannot participate in another geometric network or
other advanced geodatabase dataset such as a topology, network
dataset, terrain, or fabric.
Datsets will be unavailable to include in a network if:
- The feature class is not in the same feature dataset or external to
- The feature class participates in a database Topology.
- The feature class is already in another network (either network
dataset or geometric network)
- The geometry type is not point or line
To convert multipoint features into point features use the Multipart to Single Part geoprocessing tool.
In catalog it is difficult to discern a multipoint from a point:
Even though I know that POINTFEATURES are points and REVTABLEPOINT are multipoint features they look identical. You must right click on the dataset and get the properties to find out if the features are point or multipoint.
I have seen that when data is imported from MapInfo TAB and some CAD formats the points will be imported as multipoints, mostly with a single point for each row, to avoid the possible loss of geometry during import.