Why do only some drill bits slip out my drill chuck?
Drills do not work in reverse
The reverse setting on the tool is for use with screws and bolts, and maybe for taps if you have a power-friendly tapping situation.  It is not for use with drills.
Drills are only made to go one way, ever.
When withdrawing a drill from a hole, you are to continue running the drill in the forward direction, and pull it out of the hole while it is spinning forward.  It is normal for the drill to start to bind as you pull it out.  The sharpened flutes of the drill will make short work of whatever is binding it.  The spiral will continue to pump material out of the hole.
If you run the drill backwards, there is no cutting edge there, and so cruft and debris tends to be plowed into the space between drill and the wall of the hole.  This quickly causes the drill to bind.
With the drill binding in the hole, pulling the tool out will cause the drill to come out of the &quot;hex&quot; quick release in your tool. It is not designed to firmly clamp the bit, it is designed for quick release of screw bits.
The drill would behave similarly  in a proper chuck, by the way, but a chuck has much more gripping power.