If you use the following command: "/execute @e ~ ~ ~ tell @p Test"
it returns:
"Entity whispers to you: Test
You whisper to (Yourself): Test"
so the Entity you specify tells you "Test"
and you tell yourself "Test".

Alternative explanation:

If you execute the /tell command with an entity (/execute @e[type=Pig] ~ ~ ~ /tell @p ...)
not only the entity whispers to you, you also whisper to yourself (e.g.:
"Pig whispers to you..."
and "You whisper to Zuzu_Typ ..."
what I mean is:
the specified player is the Pig (@e[type=Pig]) and NOT me.
so I shouldn't be whispering to myself.

Updated command for 1.15.2 and 1.16:
/execute as @e[type=!player,limit=1] run tell @p Test