In a narrow sense, if you just catch a fish and don't kill it, it's not killing; Broadly speaking, fishing has caused harm to fish and belongs to killing. From the Buddhist precepts, the completion of killing requires the following conditions: first, kill the other person's heart, then take corresponding measures to implement it, and finally cause the other person to die.
If these three processes are sufficient at the same time, the crime of "killing" will be completed, which belongs to the "unrepentant" in the commandment. If you stop the behavior halfway, or if you carry out the behavior, but it does not cause the death of the other party, it belongs to "no repentance" in the discipline, and repentance can reduce or even eliminate the sin.
However, in the end, killing lives and hurting the hearts of all beings violated Buddhist teachings and cut off the seeds of compassion. Fishing, whether it kills the fish or not, is harmful to the fish and deprives the fish of their freedom. Therefore, it is absolutely forbidden for people who believe in Buddhism.