Quick Answer
Breathing underwater would make diving far easier, but it would not make humans aquatic. Water conducts heat away from the body much faster than air, pressure rises with depth, and vision and sound behave differently underwater. If humans could safely extract oxygen from water while retaining normal physiology, shallow-ocean work and habitation would become much more practical, but deep-ocean survival would still require major adaptations.
Fish solve the oxygen problem with gills, extracting dissolved oxygen from water. Humans have lungs designed for air, so simply giving us 'underwater breathing' would require a major biological change or an additional organ. Even if that problem were magically solved, the ocean would remain physically demanding.
Pressure would still win
Water pressure increases by roughly one atmosphere for every 10 metres of depth. At great depths, tissues containing trapped gas — especially the lungs and middle ear — face severe pressure differences. A hypothetical underwater-breathing human would still need physiology capable of handling pressure safely.
Cold becomes a major problem
Water transfers heat efficiently. Even water that feels comfortable for a short swim can remove body heat over time. Without improved insulation or metabolism, underwater humans would remain vulnerable to hypothermia.
Would underwater cities appear?
Possibly, especially in shallow coastal regions. Construction, food production, energy and maintenance would still be difficult, but people would no longer need a constant supply of breathable air. Underwater agriculture could also expand if light and nutrient conditions were suitable.
Communication would change
Sound travels faster in water than in air, but human speech is adapted to the vocal tract and acoustic properties of air. Underwater humans would need new ways to communicate efficiently, likely relying more heavily on visual signals and technology unless their vocal anatomy also changed.
SpeculativeThe biggest unknown is what 'breathing underwater' means biologically. A human with artificial gills, fish-like gills, or a completely new respiratory system would face different limits. The scenario is therefore about removing one constraint, not turning a human into a fish.
Evolution would eventually follow
If underwater living became normal for many generations, natural selection could favor traits involving insulation, pressure tolerance, vision, hearing and movement. Cultural adaptation would happen far faster than biological evolution, so technology would likely dominate the early transition.
Solved by assumption
Breathing problem
Still increases with depth
Pressure
Much faster in water
Heat loss
Still difficult
Deep ocean
The bottom line
Underwater breathing would be transformative, but it would solve only one of the ocean's many problems. The humans best suited to an aquatic civilization would need adaptations to pressure, cold, movement, perception and life-support systems as well.