I've seen this too - I'm going to guess there are various reasons - I'll speculate below:
- Age is a criteria used for various "adult" privileges - so I can see them making themselves "older" to achieve these, much like teenagers today change their driver's license or carry a fake to get alcohol
- On the flip side, Age is a criteria for less desirable things, like the draft. If you did not want to enter a draft situation, you might drop your real age by a few years to give yourself a chance to dodge the war and stay at home and help the family.
- Age is also a distinction for acceptable marriages - so again, you might lie a bit about how old you were in order to get a license and legally marry
I'm sure there are other reasons. As far as the month and day goes? Maybe the dude at Ellis Island made a mistake? Or wherever they entered the country, the immigration specialist is human and may have just got it wrong. Or perhaps that's his Christening month and day, but the year is wrong - or maybe it's right? Hard to say.
At least that's what I would speculate...