Ask any young Marine when the Marine Corps Birthday is and they'll all know immediately that it's November 10th. Ask them on November 10th and they may be intoxicated and/or greet you with a "Happy Birthday, other Marine!"
Ask any lower enlisted soldier what day the Army's birthday falls on. They'll probably struggle for a minute before deflecting the question and acting it like it's some obscure fact they should know for the board. Here's a hint: It was June 14th, otherwise known, at the time of writing, as yesterday.
If an Army unit throws a birthday ball, most soldiers there will probably be "voluntold" to go. Marines celebrate the Marine Corps' birthday in the barracks or long after their military service ends, no matter where they are in the world. Don't get this twisted. The Army goes all out on its birthday, it just doesn't resonate with everyone outside of the higher-ups at nearly the same passion as the Marine Corps'
There are several reasons why Marines celebrate their birthday as hard as they do. The most obvious one is that Marines take pride in every aspect of being a Marine. Even earning their Eagle, Globe, and Anchor is a tattoo-worthy achievement. The only equivalent thing a young soldier has is putting on their first unit patch. Unless it's one of the more historic divisions, it's just — like the Army birthday — another day in the Army.
Another benefit the Marines have is that the following day, Veteran's Day, is a federal holiday. A Marine can drink as much as they want without fear of missing PT in the morning. The Army would have gotten a day off the next day if it didn't receive the American flag for its second birthday — or, you know, if people actually celebrated Flag Day.
The Army could take some cues from the Marines on this one. The Corps is fiercely proud of their branch and that's something the Army should emulate. Hell, Marines are so loyal to their branch that they'll even buddy up with the Navy one day a year to play a football game.
The Army already does something to this effect on a much smaller scale at the division level. On August 12th, 1942, Major General William C. Lee activated the 101st Airborne Division and said that they had no history at that time but "a rendezvous with destiny." And it did.
That entire week, the 101st celebrates Week of the Eagle. It's a week of smaller-scale parties and sporting events that bonds the soldiers together — much more than its May 24th's Day of the Eagles on which everyone just takes part in a painstaking, slow division run. Soldiers in the 101st are proud to wear their Old Abe.
At the unit level, a simple call of "no PT on the morning of June 15th" would immensely spark interest in soldiers. Instead of knife-handing soldiers to go to unit functions, encourage them to enjoy the night in the barracks. Instead of unit runs, encourage platoon bonding events that will most likely end up in drinking. Traditions like having the oldest troop give the youngest troop a piece of cake don't have to be brought over if the Army just lets soldiers enjoy their day — their birthday.
Even little things, like Sgt. Maj. of the Army Dan Dailey's challenge for soldiers to "earn their cake" on the Army birthday a few years back, are a step in the right direction. You could even have fun with the most Army thing imaginable... impromptu push-up contests. Winner gets "bragging rights" for the year and first piece of cake.
It's wouldn't take a huge overhaul to reinvigorate soldiers' interest in the Army's birthday, thus sparking Army pride.