In your entry_date tag you're using (date formatting docs):
%F (month, textual, 3 letters)
%Y (year, 4 digits)
So it's outputting as you've entered it. If you want 19 may 2014, change %m ...
Your date format is incorrect.
Please check https://ellislab.com/expressionengine/user-guide/templates/date_variable_formatting.html.
Your format there provides (%F, long month) Feburary (%n, month ...
I believe, your options are:
to change the format of date you're using on the segment_2, which isn't a good idea because EllisLab can some day finally normalize all date fields;
to reformat the date ...
You could enable php, grab the current time and add as much time as you need, then use the start_on parameter.
Or here's a plugin you could use:
Maybe something ...
Update: Wes Baker posted, that there are "official solutions".
In ..../system/expressionengine/libraries/Localize.php around line 283 remove the following block of code:
if ( ! empty($date_string) &...
You could use conditionals and the date format function to extract the month from the date and output a different season.
Of course you would then need to define seasons by the start/end of months. ...