this is factually correct
Not early christianity. Opposition to suicide only came later as a doctrinal invention by the catholics, with the nicene creed and theologians like augustine, aquinas etc. Augustine actually articulated the first explicit condemnation of suicide in christianity, by interpreting 'thou shalt not kill' as implicitly including 'oneself', since 'thy neighbor' was omitted. If God only meant 'do not kill thy neighbor', he would have said so, according to augustine. (Then again, if God's word is perfect, surely His commandments shouldn't need to be interpreted by exegesis 1500 years after the fact? Why didn't God just say 'thou shalt not kill thy neighbor or thyself' to avoid any possible confusion? It would have saved a few souls from eternal damnation. Moreover, according to Augustine's reasoning by omission, nobody should kill anything living at all.)
He took the rest of his reasons from plato's phaedo.
Suicide only became a secular crime and actually considered 'sinful' in the 6th century, and additions like it becoming an ecclesiastical crime and denied proper burial only came much later.
I'm certainly not hedging my bets on the side of a repressed 4th century north african theologian with a penchant for sadomasochism, and a set of state laws obviously put in place by those in power to control populations through fear and intimidation.
And buddhism is actually a bit ambiguous when it comes to suicide. It depends on the intentions and the reasons. If you're just committing suicide as a shortcut to nirvana, then it's wrong and will result in more rebirth.
Then again, most intentions/desires result in rebirth according to buddhism. But suicide doesn't have some special karmic status as uniquely bad.