When I try to select an edge loop, I select one edge(Red arrow) and then from menu select > Edge Loop. But this select only the adjacent edge. Not the entire loop. Why is this happening?
I created this model in the following structure : Cube > Subdivision modifier > level 3 > Edit Mode > To Sphere. Delete one vertex from side, select the border vertices, Use To sphere. co plane them. Done.
“think” its because the vertex’s to each side are poles (?)
delete the part that goes into the sphere, then loop select the edge extrude then scale in a tiny bit then do the tube going into the sphere
ps hold alt key when selecting and it does the loop select
heddheld is correct, the reason a pole (more or less than 4 edges meeting at one vertex) disrupts the ability to select an edge loop is because there are actually more than one edge loop that could be selected. basically it could select the loop you want ( the hole) OR it could select the loop that goes along the latitude line of the sphere. since the two loops aren’t disambiguated, the tool can’t tell which one you want to select.
Don’t clearly understand this part, but I get with the explanation with @atartanian I understand why the loop tool isn’t working.
I don’t know why you want me to extrude, won’t doing it result in 5 edge on a vertex again?
I am sorry if I sound silly. But I want to make sure I understand clearly.
This is the selection you are mentioning, right?
pic should explain I think
it just gives a clean edge loop on the hole
will help with any smoothing later on too
Got it. Thanks! 
