Why is my attribute table edit button greyed out?

This can happen if you don't have permission to edit the layer. Outside of QGIS, open the folder that the layer is in, right-click on the layer, and open Properties > Security. Where it says "Permissions for [username]" there should be a check next to "Modify" and "Write." If not, change the permissions for that file. If you don't have permission to change the permissions (a rather infuriating logic loop), save a copy of the layer to a folder that you can edit, and work from the copy.

I had the same issue when I added the shapefile by Add vector layer - browsed to a zip file and then selected the shapefiles it offered. When I unzipped it, went to Add vector layer and directly selected the shapefile I want to add (as opposed to the zip file), the Toggle Edit option became active.

Try "Toggling editing" from the right click menu in the Layers Panel BEFORE opening the attribute table - it worked for me!

In my case, layer was "read-only" in Project-Properties-Data Sources

You have to save the layer, for instance I add data from a *.csv file and you will work perfect with that data but if you don't save the layer as a shapefile using right click > save object or similar (I have qgis in spanish) you are not going to be able to edit it.

I have come across this issue. The easiest way worked with me is check if you have primary key in your data. If not, add one and reload the feature and try editing. But because shapefile does not have a primary key concept, you can use field calculator to create a column that utilizes row or record number as its value.