In X-Men: Apocalypse we get confirmation from Pietro that Magneto is his father, and he (Pietro) knows it. However, he never mentions this fact to Magneto. Wouldn't this be something he would want to do when the two of them were together?
Is there a reason given in the movie why Pietro wouldn't bring this up at any point?
To directly answer your question...
No. There is no reason given in the movie as to why Pietro wouldn't tell Magneto he was his son.
If we were to speculate there could be numerous reasons. My own thought on it is that he didn't want Magneto to stop what he was doing just because his son asked him but rather wanted Magneto to stop because it was the right thing to do.
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.
