^ If you mean "artificial" in the sense that I didn't grow up in New York and thus "shouldn't" be rooting for New York teams, then yeah, I suppose you're right. (I "should" be a KC Royals fan since I live within their territory, and their AAA affiliate is in Omaha)
If not, then what?

If you're saying I'm not sincere just because I root for both Yankees and Mets, then you're wrong.
I'll try and take another crack at it:
IMO, it just seems kinda fake and forced, having more than one favorite team (per sport), especially if they're rivals. Just not natural. Not exactly because you're not from around there, as plenty of people root for out of market teams, or are transplants living elsewhere, etc. Kinda like when, back in 2007, you were a big Yankees fan, and then once they lost, suddenly you were rooting for the Red Sox. Just doesn't seem right.
Some of that might be because the majority of any team's fanbase are local to that area, and grew up around the rivalries (some stronger than others). While the Yanks and Mets don't play a lot, they DO play every year, and have competed for titles. They also spend the rest of the year competing for attention in the NY market, trying to one-up each other on players (Mets are way outclassed there), and the Mets also claim more of the Long Island crowd, whereas the Yanks get more of the city-dwellers.
Some of it also plays to the term "fan" (short, of course, for "fanatic") in the first place. To be fanatic about more than one team, playing the same sport in the same location, and competing against each other every year, just seems "off" or forced. You're clearly more of a Yankees fan (your avatar, your attempts to identify yourself as a Bleacher Creature, etc), but claim to also live and die with the Mets. Most of the time, both games are happening at the same time, so it would seem you'd have to be a lesser fan of BOTH teams in order to follow them. You're either watching one game while checking highlights of the other, or you're flipping around based on scores, matchups, or whatnot and not really paying enough attention to either.
Another pet peeve on the subject (and not necessarily about you, but in general) is people that seem to pick their teams just because they are frontrunners (the people, not the teams). Everyone knows these guys. You can identify these people pretty easily, for the most part. If they identify with more than one sports team that's not local to them, figure out when they started watching the sport. Just fans that want to root for the winners, so they can always talk shit to other fans. Oddly, people picking an artificial "favorite" team rarely pick a loser, or even a team with a likeable player that's having a bad year. They'll claim they picked the 49ers because they liked Joe Montana, but the titles didn't hurt. A few picked the Dolphins for Marino, but they weren't winning titles, so not as many picked them.
You know, the guy that started following sports in the 90s, and is a Cowboys and Yankees fan (or maybe Blue jays, depending on when in the 90s). The guys with no connections to Pennsylvania or California, but root for the Steelers or 49ers. New England is dealing with it's own "real fan vs pink hat" issues because this decade has had the Patriots and Red Sox both in yearly contention.
Because the Yankees have so many championships, and always spend enough money to be in contention, most frontrunning baseball "fans" are Yankees. Could be part of why you get questions about it, because you artificially picked a team, and it just so happened to be a yearly contender with a ton of rings. Even cheapens it a little because you hedged your bets and picked TWO teams in a big market, so pretty much guaranteed you'd be able to root for a decent team and talk shit about your team every night. Just feels forced. Hard to judge your "fan-ness" anyway, as you picked your teams recently, and the Yankees haven't ever really been "down" under your watch. Another thing that gets you, though, because you weren't there in the lean years, suffering through shitty teams and mis-management (definitely right now with the Mets, but you're split with the Yankees, so you always avoid heartbreak or being out in May/June), so it questions how much you "deserve" the wins. A fan that picked the Red Sox after their big run in 2003 probably enjoyed the 2004 title, I'm sure, but it's not quite the same experience as someone who spent a lifetime waiting for it, or watching shitty games with your father or grandfather, and then finally getting it after 86 years.
Hell, the Tampa Bay Rays "fans" are the perfect example. they're in the playoffs, suddenly the stands are full and every douchebag has a cowbell. They lose, and then can't fill the stands for a Yankees or Red Sox game in a pennant race. They want to claim the win, but don't want any part of the loss, or just want to be seen as a fan if it's popular. If you'd picked the Pirates as your baseball team (dear god, talk about having to WANT to suffer), you probably wouldn't hear a lot of cheap shit.
Not trying to come down too hard on you for all this, just trying to throw out some of the things that cause you to catch a little grief about this on here.