In order to group by date, they have to be valid date entries. You could have a valid date entry, or what looks like a date entry, but is really text (and with text, you could enter anything).
Date functions/operations only work on valid date entries.
Dates in Excel are really stored as numbers, specifically the numbers of days since 1/0/1900. So they are really just numbers with special date formatting applied to them.
An easy way to check to see if you have a valid date entry or a text entry is to apply the ISNUMBER function on it.
Let's say that your entry is in cell A2. Then in any blank cell, enter this formula and see what it returns:
If it returns "TRUE", you have a valid date entry in cell A2. If it returns "FALSE", you have a text entry in cell A2, not a valid date entry.
You would then need to convert all your values in that column from Text to Dates. You can do that by using "Text to Columns" on that column, choosing the Date option with the proper date structure (appears to be "DMY" in your example).