We did "cry it out" at 8-9 months. You don't literally abandon them. We'd start by leaving for a minute, then 2 minutes, then 3 minutes, and so on. It took about 10-12 minutes the first night before they settled, shorter the next, still shorter the next, and by day 4 it they were fine.
People just won't get it unless they have kids, I don't see any way to explain it otherwise. Even then, some people will have some unicorn baby that is magical to raise. Teaching your child to self sooth is such an important skill.
I understand that parenting is hard. However, I can't help but be sceptical about the "self-soothing" theory - how do you know that infants aren't simply feeling helpless and stop crying because they feel that nobody is coming?
This is an open question, I'm not taking any side because I don't know. But any answer should be supported by some kind of rational argument, not the argument of convenience, i.e. my child stopped crying, therefore they're okay, because I feel better when they are not crying.
This is why people opt for gradual extinction, it allows you to comfort them and establish that parents are still around. By a certain age they have the capacity to fall asleep on their own, but are still accustomed to falling asleep before being put to bed (ime this was because we would feed-to-sleep, probably the mistake that led to having to sleep-train later, and it's possible that it could all have been avoided if we started the evening feed slightly earlier with the lights on by the time they reach 5-6mo). The goal is to provide comfort while allowing them to learn to fall asleep autonomously, or else you're looking at waking up in multiple times a night to hold them indefinitely, and that is unsustainable for working parents, nor is it particularly restful for the baby.
I'd expect that going from one extreme to the other (i.e. extinction) can lead to long panic crying and is unnecessarily harsh. By contrast if you rock your baby until they are comfortable and drowsy (but awake), then set them down, they'll be annoyed at the adjustment at first and protest but won't freak out. Then you can decide on whichever interval you want to check in (5-10 min), usually touching but not picking up. By the first night our kid fell asleep in 15 min, then 5 min the next. Then in no time he's sleeping through his nights.
Everyone gets better sleep and it was fairly painless. It doesn't have to depend on an infant feeling helpless - at bedtime they have high sleep pressure, they want to sleep. We told ourselves we'd abort the process if it things went awry. In the daytime they're as happy as ever.
