Hi, I used SelectByLocation geoprocessing object in c#. 
                selByLocation.in_layer = lyConvexLine;
                selByLocation.select_features = lyConevex;
                selByLocation.overlap_type = "INTERSECT";
                gp.Execute(selByLocation, null);
                
                selByLocation.in_layer = lyConvexLine;
                selByLocation.select_features = lyPairLine;
                selByLocation.overlap_type = "WITHIN";
                selByLocation.selection_type = "REMOVE_FROM_SELECTION";
                gp.Execute(selByLocation, null);
 
above code worked well. However, in other part of same code, SelectByLocation did not work at all. 
                selByLocation.in_layer = lySelectedPoints;
                selByLocation.select_features = lyTempPair;
                selByLocation.overlap_type = "ARE_IDENTICAL_TO";
                gp.Execute(selByLocation, null);
 
After above part, nothing happend. I checked number of selected object by GetCount, and even CopyFeature tool, but nothing was selected. THe only difference 1st and 2nd code is: at 1st code, layers were polygon and line, at 2nd all of two layers were points. But SelectByLocation meant to be worked well with point as well, right? I test other overlap_types... all of them failed. My features are not broken. I checked those features inputted to selectByLocation manually.