It works as intended for me and I am using Office 365. Which Excel version you are using? Maybe implicit conversion is not being done in your case.
So first convert the date as Text in column A to the real dates and to do that you may insert the following formula in any blank column in row2 and copy it down for all the dates in column A and then either copy all the dates generated by the formula and paste back as Values in column A or refer the new column with real dates in the formula and it should work for you then.
Also, you don't need to insert a column with Today's Date, you may just use Today() function directly in the formula.
In the attached, you will find several ways to find the difference in the dates other than Network days.