You can breathe pure oxygen - it's all a question of partial pressures.
0.21bar O2 is what you breath normally, you can eithge rmake the rest up with Nitrogen or reduce the pressure and breath pure oxygen.
At about 1bar 02 (ie. breathing pure oxygen at atmospheric pressure) you get slight lung irritation after about 24 hours.
At higher partial pressures oxygen becomes toxic - it effects your centrla nervous system. The limit depending on who you work for, how much physical activity and how much danger you are in is between 1.4bar and 3bar. So recreational diving you would limit O2 to about 1.2 bar, either by having 40% oxygen at 3atmosphere of pressure or 21% at 6 atmospheres, you can handle upto about 2.5-3 bar if you are safely strapped down in a chamber.
The effects of short term exposure to high O2 aren't necessarily themselves dangerous, you get muscle spasms with CNS but if you are 100m underwater this can be dangerous.
The reason for complicated gas mixes ( nitrox/trimix/heliox) in diving is to achieve the pressure of the surrounding water while keeping the partial pressure of biologically active gases, especially oxygen, low enough by diluting them with inert gas.