You think maybe there is a relationship there between Skye and May or perhaps Skye's mom was a "rogue" agent?
I hate making predictions about TV shows because no matter how much a series might be "planned out", the writers could get together at any moment and decide to change or ignore something they've been building up for the entire season.
To be honest, the main reason I ever started thinking about this weeks ago was because I found out that the actress who plays Skye is of Asian heritage. Somewhere in my head I thought "it would be interesting if Skye and May were related..."
I dismissed that as being too obvious a twist. And just because it's probably what I would do if I was writing the story doesn't mean it's the best idea.
But even ignoring that shit, the seem to be going out of their way to make May overreact to Skye's curiosity about her parents. Which suggests some kind of deeper connection between the two. I dunno what kind of connection it is, just like I dunno what connection exists between Red and Lizzie in The Blacklist. But like that show, this one has to be significant enough for the audience to give a shit when it is revealed. But it can't be so obvious that the audience is like, "well, duh".
Maybe May is the one who cacked Skye's mom. Maybe she was her mom's S.O. I dunno. I'm just saying there's some sort of connection there which is driving May's response to Skye. Not just with this particular research, but Skye's presence on the team in general.