I hear this all the time from 'coaches' and 'arm chair experts'.
Being able to breath bilaterally (on both sides) is definitely a skill that needs to be developed. Breathing bilaterally has benefits such as
People who only breath on one side tend to have an asymetrical body roll and position - typically rolling more on the breathing side. This means than on the non breathing side they typically have less lat muscle and more deltoid engagement (using a smaller muscle). They often mention feeling less strong on that side. Balance (or lack of) makes it harder to swim in a straight line especially with no black line for reference.
Responding to conditions
Imagine you are swimming straight along a beach and you have trained only breathing on the 'ocean' side. Any type of swell and you end up sucking a lot of water. Being able to change sides means you breath where the conditions are easiest.
Similar to above if you are swimming down a beach and always looking out to sea how will you know when you are near the turn buoy without constantly looking up (hint - look for land marks on any open water swims rather than relying on sighting the buoy.
If you swimming close to someone on your breathing side breathing on the other side turns your face away from them reducing the risk of being hit.
So if bilateral breathing has all these advantages then I should breath every third stroke ?
Bilateral literally means both sides. There is nothing that specifies every 3rd stroke (commonly called "breathing on the three"). Every person is different - everyone has different lung capacities, different hematocrits, different VO2, different stroke efficiencies, different turn over rates (cadence). The need for air can also change during an event as your pace changes.
Bilateral means you CAN breath both sides.
Some people breath every second stroke. For most of a race I will actually breath every four strokes. I find that if I try and breath every second stroke it is borderline hyperventilating but everyone is different. The key is though that even though breathing on an even number means you are always breathing on the same side that side will change based on conditions. During a race I may switch sides (but still breath on the same count) based on conditions, seeing where people are, protection etc
If you have a look at this video of Kieran Perkins winning Gold at the 1996 Olympics you will note that he is breathing every 2nd stroke BUT he changes sides so he can see where his competition is in the pool.
Being able to breath on both sides is definitely a skill you should develop but do this based on a breathing rhythm you are comfortable with. For example if you set is 10 x 100 do them alternating sides each interval - or even go up the pool breathing left, down the pool breathing right. Develop the skill without forcing yourself to breath every third stroke. Practise breathing both sides using drills - you will find that if you cant breath on one side it means there is an issue with your stroke on that side. Have someone check out your stroke and see what's causing the issue