@S W Randall
As 'Dennis' has already proffered ...
There appears to be currently a problem/issue with "Tagging" using a computer "Mouse" (and, particular "Browsers"); whereas, such "Tagging' IS working with a "Touch Screen"; and, the "Mobile Application" of "Family Tree" of 'FamilySearch'.
Plus, there also appears to a similar problem/issue with regard to "Correcting" the "Indexed" records in "Family Tree" of 'FamilySearch'.
Here are a few recent posts raised in the 'FamilySearch' ("GetSatisfaction") 'Feedback' Forum on the matter:
Index corrections are broken! ... [ 16 Days ago ]
Person Tagging on FS Memories for Image files - appears to be plain BROKE ... [ 2 Days ago ]
No mouse input accepted on images ... [ 2 Days ago ]
Plus also in this Forum a few days ago:
'Group' = FamilySearch Family Tree
Person tag process broke - when dealing with image files.
I hope this helps.
There is currently a bug in the system they are working to fix
in the mean time - you can probably use your "touch screen" to initiate the creation of the tag instead of your mouse.