If you dry fire Kahr's, the firing pin may or may not be protruding from the breech. It retracts when the slide comes forward. With the 380's, there is not enough space to allow the pin to retract if it is protruding and as you found, the casing gets hung up on it. What to do. Before inserting the magazine: Either turn the gun over and simply pull back on the 'foot' of the striker (it is not under tension) OR rack the slide 1/4 inch or so to reset the striker before locking the slide back to feed the first round. Kahr has cautioned me in the past about damaging strikers by not being careful so your's may break. I'm pretty good now....even with lakeline's 'stiker for life' solid steel version. Your first round should feed easily....what ammo were you using?
Welcome to the forum from NC!
Kahr P380 x2
Kahr K9
Kahr CM45
Sig P938
Sig P365 x2
Sig P322
1911 Range Officer 9mm
M&P 9mm