Life in the ancient Rome

That is not true. One could only become free if the slaveowner agrees to such terms as in they just set you free or work for freedom. It didnt mean the owner had to do that anyways. I would imagine many didnt as there was no incentive to do so on the part of the slaveowner. Where is 'many' were prior slaves. I would like official documentation as in proof not just what someone says or guesses even historically. Were there records showing 'most' were freed slaves?
I'm not sure if it's possible to know what's true per say, but there's good evidence for manumission being common in Rome.

Here's a debate on Roman Slavery and the Rate of Manumission. The Roman Republic and Empire were around for a long time, therefor it depends on the time frame.

Apparently, freeing slaves in an individual's will had become so widespread in the late Republic that in 2 BCE the Lex Fufio-Caninia was passed limiting the number of slaves a citizen could free in their wills.