I think the concept of a "month" stems from the fact that Gay Pride Day is actually June 28 (the anniversary of the Stonewall Riots, and the birth of the Gay Pride movement), and it's difficult to have so many events on one day. On my little island, we have always had celebrations mid-June, so as not to conflict with the New York City event at the end of the month.
BUT - (in the US) Veterans Day (formerly Armistice Day - "the 11th hour of the 11th day of the 11th month" - the end of WW1) has Veterans celebrations and recognitions all month long, for exactly the same reasons as for Pride, making the month of November essentially Veterans Month.
Also, with the proliferation of various other "months" and "days" (see above - Mental Health Month, Men's Health Month, and my personal favorite, Pet A Cat Day on June 5th), unless we find a way to add about 102 more months to the calendar, there will always be overlapping and extended celebrations.