Frankly, It's None Of Your Business
You are forgiven if you are not sure who Millennials are exactly, since even Wikipedia doesn't know: "Generation Y, also known as the Millennial Generation, is the demographic cohort following Generation X. There are no precise dates for when Generation Y starts and ends. Commentators use beginning birth dates from the early 1980s to the early 2000s." So for the sake of argument, let's say they are about 25 to 30 years old.
Ironically, the Strauss–Howe generational theory predicted Millennials would become more like the "civic-minded" generation of their grandfathers, "with a strong sense of community both local and global." Guess not when it comes to "sharing" on social media.
Finally, something a 30-year-old and I can agree on. Who in the hell cares about telling others what you bought, and why? I find the more word gets out that I bought something major (say, like a car) the more I get bombarded with offers that I don't need or want, from aftermarket products to satellite radio, from insurance to extended warranty offers (not to mention never-ending emails from the dealers whom I asked for a quote). Moreover, I don't feel like it's really anyone else's business if I bought a Toyota or a Ford (except the automakers themselves, although it doesn't take long for the warm glow toward a new buyer to turn into a chilly reception from service or warranty.)
I understand my kids wanting to post pictures on Facebook, since they can do it once and have them seen by nearly all of their friends, but why would anybody want to broadcast the fact that they bought something? I find all of the "share us on social media" pleas from retailers tiresome and wouldn't do it -- just because they asked. I tend to communicate one on one, say, with a neighbor who sees the new car in the driveway and asks me what I think of it. He will get an earful (good and bad), but I am not going to give a bunch of strangers the same information.
I am very happy to recommend the hotels I like in Paris to a friend heading over, but not so interested in trucking over to travel sites to "share" my thoughts with anyone who wants to research that hotel. Then it fills up with all of the wrong people and ruins it for me and my friends. Similarly, if I buy something I think is really great, like "Younger Next Year," I will make a point of telling personal friends, but never post to social media.
If you read the comments on most retail sites you have a pretty hard time sorting through the ones bought by the manufacturers (not hard to do) and those of real customers. Even then, you often get diametrically opposed views. Whom do you trust? Whose voice is authentic? How do I know this guy has the same taste I do?
In a similar vein, I don't trust the motivation behind "sharing" purchases on social media. If I got a tweet from one of the folks I follow and they talked about just buying a new coat or seeing a new play, I would think they had lost their minds (or were part of a paid promotion, shame on them.)
What I buy, where I buy it and why is between me, the retailer and American Express (and I suppose the NSA). Share that.