To insist on something; to assert firmly and refuse to back down.
彼は間違いだと指摘されても、最後まで言い張った。
Even when his mistake was pointed out, he insisted until the end.
子どもは「やってない」と言い張って、なかなか認めようとしなかった。
The child insisted, "I didn't do it," and wouldn't admit it.
証拠が揃っているのに彼女は自分の無実を言い張った。
Even with the evidence, she maintained her innocence.
会議でそんな意見を強く言い張るのは得策ではない。
Insisting strongly on that opinion in the meeting is not a good strategy.