Not hard for rim to cut into valve stem if you're hamfisted.

Valve cores can leak, even new ones. The only sure way is to buy a bunch and swap them into a known-good tyre, then when they're tested to hold pressure for a few days take them out & store them for future use.

Valve stem inside can also cause leaks; the thread can stop valve from screwing in completely - use a tread tap to clean the thread. The conical seat might not be sealing fully against core - again there's a seat reamer you can use.

​​​​​​​Core is screwed in firmly but don't overdo it... everything is a soft metal in there, not hard to wreck something with too much torque.