Because it's emotionally difficult to deal with his literal daddy issues. From an interview with Evan Peters, the X-Men Quicksilver, on the character motivation:
Evan Peters didn't say too much about Quicksilver and Magneto's relationship in the movie because he didn't want to give some things away but he did hinted us with a little bit of a drama moment between the two.
Evan Peters: It’s tough, man, it’s a hard thing to meet with an estranged father. It’s a very difficult thing. It’s a very real thing. So it was interesting to play that side of Quicksilver.
Ask anyone who has been adopted and decides to track down their birth parents (or not, an equally difficult decision).
Pietro was also dealing with his own young adult identity crisis.
Evan Peters: It's a big motivation for Quicksilver to get out of his mom's basement. He's trying to find his father and help him out.
In the film, there is the scene where he relates how Mystique's 1963 saving of President Nixon affected him, talking about he's still a loser living in his mom's basement.
In short, too much emotional turmoil in a difficult situation. Seeing his father, face to face, after realizing he is his father too late last time, he froze up like a deer in headlights, and ran off. A typical fight or flight response for someone still maturing.