Aup. Do you know why this website reference says Sanyuktha nikaaya 44.9 as reference? To me that's a strange reference. Just asking if you know.
The translation is not quite right anyway.
Nevertheless, maybe I could make this sentence a little clearer to you since you have asked this question.
1. It does not say "reborn". Reborn is the translators own personal interpretation.
2. It only says that the being or in other words the "living being" (saththo means animal as in any living being from the animal kind is called an animal).
3. This living being leaves a body and has not "come" to another body.
4. At this point it could be that the animal or being is "caused" to not do so by greed.
It doesnt really say "reborn".
Nevertheless your dilemma of Anatta and Atta is not a concluded argument. It was always debated and theorised in many ways. Anatta remains a dilemma. But if you read the Anatta suththan in the same sanyuttha nikaya you will see certain things have been said as explanation to what Anatta actually means. It means your looks or image is anatta. No soul. Your pain is "no soul". Your intellect is no soul.
I think one of the problems with this type of websites is that the reference is giving some weird number like 44.9 etc etc without the actual chapter name. The Anatta suttan is in anichcha vaggo. Anichcha means "uncertainty". So if you read the text with that in mind you can understand Anatta has something to do with uncertainty. When you live you should know that your death, health, state of hermit-hood or chastity of being a pavidhi or monk is also uncertain. When you die, what takes place is also uncertain. Thus, my personal opinion is that Anatta is a teaching established to make sure you shed all of these worldly certainties, ego and greed. You have no soul. What nonsense are these things like greed and certainties? They are utterly useless, nonsense. That's the teaching of the Tipitaka.
Edit: I will tag
@crossfire to this reply if you don't mind because he referred this page directly.
Cheers.