Does the billiard game support such a rule?

I was playing a billiard game in my home town in Canada and collided with one such a very surprise to me rule that I was arguing about, and because of

I was playing a billiard game in my home town in Canada and collided with one such a very surprise to me rule that I was arguing about, and because of this cold not finish the billiards game. So the thing was when right in the beginning of the game I chanced to simultaneously score 2 balls, which one was striped and other was a white one... The thing is that by scoring a white ball I knew that I had to miss my shut by letting my other opponent to make his turn, but for being played billiard for a long time, I always kept the rule that if right in the beginning you already scored any type of ball, no matter if with the white one or not, you have already made the decision for yourself to score same kind of balls, but only right when your turn comes up, however, my opponent said that because I scored my chosen ball with the white one that mean that he has the privilege to decide by scoring any types of ball after that, so which one of us is right?

or:I was playing a billiard game in my home town in Canada and collided with one such a very surprise to me rule that I was arguing about, and because of this cold not finish the billiards game. So the thing was when right in the beginning of the game I chanced to simultaneously score 2 balls, which one was striped and other was a white one... The thing is that by scoring a white ball I knew that I had to miss my shut by letting my other opponent to make his turn, but for being played billiard for a long time, I always kept the rule that if right in the beginning you already scored any type of ball, no matter if with the white one or not, you have already made the decision for yourself to score same kind of balls, but only right when your turn comes up, however, my opponent said that because I scored my chosen ball with the white one that mean that he has the privilege to decide by scoring any types of ball after that, so which one of us is right?

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