This question comes up frequently on my pen turning discussion forums. I don't know if drill presses just do not like pen turners or what. But, as said, the holding is (usually) friction with the Morse taper fit. First, clean out the inside of the receiving taper with a cloth or paper towel lightly oiled (WD-40 works great). Do the same with the male taper and try again. To seat, open the chuck all the way so the jaws are not protruding then, with a wood or rubber mallet, whack it fairly firmly into the receiving taper. Sometimes the tapers just do not want to mate respectably. Even though they are milled to a standard set of tolerances, there can be just enough difference so you may never (very rare) get a perfect seating. I'm about to buy a Morse taper finishing tool just to true up all mine and keep them that way.
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