It is not exactly the reason but still related to the pressure. In SCUB or surface-supplied diving, the air that the diver breath has the same pressure as the level that the diver is, called ambient pressure. That means when the diver is let's say in 20 metres, they consume 3 times more air in quantity (but volume is the same). This has three consequences as the dive is deeper. (1) It requires way more and bigger SCUBA tanks (there are also closed system devices that cycles gases that are not used called rebreathers to address this issue but they are a bit risky) or stronger compressors (in surface supplied diving). (2) oxygen is toxic over 0.8atm (there is also time as a factor, here is an oxygen toxicity table so we need to decrease the percentage of oxygen and increase other (inert) gases. (3) inert gases do dissolve more in the body tissues and blood during compression (when their pressure increases) and does not leave body as fast so create bubbles that results in clogging arterials and damaging tissues and organs (which we call decompression sickness). We have a solution to all these problems in deep diving what we call saturation diving. You let divers to dive in chambers and let them decompress in these pressurised chambers for weeks after the dive on the vessels. In scuba diving, we do stops in ascending.

In Abyss, they were supposed to dive to a depth that was not done before so, it would require a lot of pressure and inert gas. Also it would be quite difficult to arrange the mix since the percentage of oxygen in the mix should be quite low to prevent oxygen toxicity. Instead, they use a liquid that they can control the mix of gases in it. They also do not need to use huge amount of gas since the diver does not need to breath in ambient temperature.

One last fact: the scene that a mouse is put into liquid and it is breathing inside liquid is a real scene without any visual effects (link here). They used a liquid that can carry enough oxygen and submerged a mouse into it.