He hasn't learned about the school, because he didn't ask anyone he knows about mutants. For one thing, he didn't want people asking why he wanted to know, but... mostly, he just didn't want to share this. He wanted to find out for himself what was going on, and while the internet was by far not unbiased or unopinionated, at least it had multiple sources, which made it more well-rounded than the handful of opinions he'd get from his teammates or Fury. (Plus at this point, he trusted any 'facts' he received from the Director about as far as he could throw them - before the serum.)

Unlike Rogue, Steve has no compunction about sharing information that hasn't been made public: namely, his identity. Although he thinks it'll get out eventually, so far the news is still reporting on the devastation of the city, and while 'superheroes' are still being hotly debated and talked about, the fact that a man seventy years' dead/lost to war hasn't cropped up yet. (He's sure it's just a matter of time; he knows how gossip works.)

"Remember I was dressed up like Captain America during the Battle?" he asks dryly. "I wasn't wearing the costume just for fun. Trust me, it's never been a fun costume to wear. I told you I was in a war. I was in World War II. I'm the... well, the 'original' Captain America, I guess. God, I hope there haven't been any others..." He mutters the last to himself, frowning at the table.