Slave galleys were rare in the ancient world, and became common only in the 16th century. Most rowers before that point were free men from the lower classes. In classical Athens this class of people would often push for war out of economic self-interest, since they could earn a better wage as galley oarsmen than from tilling the fields or other peacetime jobs.
Using slaves as rowers was avoided for the following reasons:
- It's less efficient. The usual way to employ free rowers was alla sensile, in which each rower had his own oar. That maximizes the sum of oar blade wet surface and thrust created. The only way to employ slaves was alla scaloccio, in which several rowers were chained to one oar. This style required less skill, but was also less powerful. It was estimated that three slaves were required to replace two free rowers. Also, the weight of all those chains will slow down your ship. Some nations, like Venice, never adopted galley slavery, relying on free rowers and the alla sensile style until the end of the galley era.
- Free men are more motivated to improve their rowing speed, learn special maneuvers and other useful maritime skills. The Trope Codifier Ben-Hur (1959) is actually a good demonstration of why the ancient Greeks and Romans did not use slaves for galleys: the poorly-treated slaves row slower than professionals, and when their ship is in danger of being rammed, they panic and stop rowing, making the ship a sitting duck.
- It puts you in a worse position if you get boarded (which was frequent at the time, since it was one of the few reliable ways to defeat a warship before powerful cannons.) If your ship full of free rowers is boarded, they'll defend it with the rest of the crew. If your ship full of slaves is boarded, they'll cower in fear at best and start an impromptu mutiny at worst. During the Battle of Lepanto in 1571, troops of the Holy League were able to free and arm large numbers of slaves while boarding Ottoman galleys, enlisting their help to turn the tide against the Ottomans.
- Maintaining even the most basic hygiene is next to impossible when men are chained in place 24/7, since they can't lean out of a porthole or go to a privy, leaving them sitting in their own feces. Between that and the constant whipping... well, you can imagine a lot of sickness and death. Trying to clean up the mess, quarantine the sick or even remove the dead will require you to get close to the slaves and possibly unchain them, which is very dangerous. Valuable slaves will die like flies, making your vessel progressively slower as the voyage goes on. Plus there's the risk of disease spreading to the rest of the crew.
- There was also the fact that most ships were simply too small. While the Mediterranean had a host of large warships, most day to day ships were much smaller, and in the contemporary Baltic the Longship was neither so long nor large, generally fitting fewer than 100 people and usually less than 50. Trying to employ crews consisting of a sizable number of unwilling slaves would've been unworkable.
This all began to change in the Renaissance for various reasons. Firstly, the collapse of the Roman Empire shattered the political unity of the Mediterranean Basin, meaning that the successor navies couldn't be anywhere near as picky about recruitment as the old Athenian or Roman Navy, while also producing a lot of opportunities to capture slaves in piracy or warfare. However, the second important feature would come centuries later, with the development of artillery, particularly cannon-bearing warships. This meant that tactics and ship design shifted from boarding or ramming to blowing ships away from a distance, decreasing the need for all-willing crews. This coincided with the apex of the Ottoman Empire, which benefited from gifted naval commanders, skilled ship design, and an extremely plentiful supply of slaves, which let it use slave galleys to great effect, in turn incentivizing its rivals to copy the method. The time of the slave galley came to an end in the 17th century, as the increasing power and cheapness of sailing ships made galleys obsolete (this had been going on for centuries but finally reached a critical mass in the early 1600s, with purpose-built sailing warships able to outgun and outmaneuver virtually every galley).
It's also worth noting that galley slavery was largely a Mediterranean phenomenon (with some carryover in the Red Sea, Indian Ocean, and the Spanish Antilles). It was a specific marriage of cheap, available slaves (and traditions of using them), the dominance of cannon-centric galley warfare, and their ability to compete with all other kinds of warships that led to the Galley Slave heyday. While oared warships were common enough elsewhere and outright galleys were used in the Baltic (indeed coming in vogue around the exact time they started to wane further south), they either had to compete with similarly-powerful sailing ships or lacked the tradition and availability of large numbers of slaves to use.
