Most swimmers favour breathing on one side. You can train yourself out of this, but it takes time and may cause more problems than it solves.
In theory, bilateral breathing should balance the roll of your body as you glide through the water. In reality, you may find it much harder to control your technique on your less favoured side.
If you’re not sure whether your breathing style is detrimental to your technique, try swimming with a centre snorkel.* This eliminates the need to turn your head to breathe.
Note how you are aligned in the water – are your legs dragging? Is your stroke symmetrical? Now try again, varying your breathing style every few lengths – try your favoured side, your non favoured side and bilateral. Does your stroke feel smoother with a particular style of breathing? Does your speed change? Does your stroke count change?
If I don’t pay attention I find I roll too much when breathing on my right (non-favoured) side, which creates a braking effect and makes my stroke uneven. I can iron it out when I concentrate but if I get tired it creeps back. You can see my problem very clearly in this shot below, taken before I had really noticed it was an issue. My head is really raised out of the water, which is probably causing my legs to drop and slowing me down. Don’t do this!
Experiment with what works for you. Ideally you should be breathing bilaterally but it’s OK to be different.
* Not all pools allow snorkels. You’ll probably get away with it if you look like you know what you’re doing but be prepared to be told to take it off.
For more advice on good breathing technique this video from Effortless Swimming is great. Don’t be put off by the super fast pros!