Your Javascript code is not passing an array of strings. It's passing an array of objects, each containing multiple properties.
For example, instead of sending:
["One", "Two", "Three"]
you're sending:
[
{
"Column1": "One",
"Column2": "Two"
},
{
"Column1": "Three",
"Column2": "Four"
},
{
"Column1": "Five",
"Column2": "Six"
}
]
There is no way for ASP.NET to map the data you're sending to an array of strings.
Either change your Javascript code to send the array that your action is expecting; or change your action to accept the data that your Javascript code is sending.