I try to create buffers of 5m on the selected points only (in ArcGIS 10.3):
The problem is that the buffer tool create buffers for all the features, why is that?
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It is important to keep in mind the difference between data sources and layers. Layers are constructed upon data sources, but they have a Query Definition property which defines the maximum rows available, and a Selection Set which defines which features are highlighted.
(You can also "Drag-n-drop" data sources from the Catalog window.)
The difference in behavior you are seeing is based on whether you have a layer or a data source in the Input Features picker:
For example, if I open the attribute table of the "cities" layer and query all cities with "Lake" in their name:
There are times when it becomes necessary to create a temporary feature class by exporting the selected set to a new feature class, but for the most part, layers have rendered that requirement obsolete (you just need to choose the right Input Features).
ArcMap usually works correctly but sometimes not. Try restarting software and/or computer.