Fetching details from the dictionary...
to press a question; to cross-examine
刑事が容疑者を問い詰めた。
The detective pressed the suspect with questions.
上司が部下を厳しく問い詰めている。
The boss is grilling his subordinate.
彼女は理由が分かるまで相手を問い詰める。
She cross-examines the other person until she finds out the reason.