Harry here you are something about a Pin vice.
1. the front view of the tool without a drill when the cap is tightened.
2. the front view of the tool when the cap is unscrewed a little bit.
3/4. the drill bit put into the tool and tightened.
Your problem can be caused by the "jaws". Actually these could be set for a few diameters only.So it means that these should work from 0 diameter ( the cap tightened fully) and to maximal diameter for the tool ( the cap unscrewed almost totally.Sometimes these "jaws" can't be squeezed fully. It can be for some reasons. The "jaws" are old and used, the cap can't be ( or isn't ) tightened fully, the "jaws" are for thicker drill bits.In many cases these "jaws" can be replaced as these are available with the tool set. If not , drills with thicker holding ends have to be used.
5/6. Maximal diameter for my Pin vice drills is 1.5mm
BTW....the cap is tightened right but unscrewed left with one hand holding the tool body with the second one.