There is no effect without a cause. For the reason you were born here and exist you will be born and exist in the future until you will destroy that cause and not exist anymore and be in nirvana. The thing that decides your conditions of existence is karma. The reason why it is karma is not possible to find out using intellectual thinking but only by meditating and finding that it is true/false within yourself. That is the official budhist view on this problem. If there could be proven using intellectual thinking that karma is the law that decides the conditions of your existence we would live in a world of saints.
Also nobody said we had an infinite number of rebirths before this. We had a big but limited number of rebirths. (about your quote, does 4 oceans seem limited or unlimited?) The reason why you came into existence in the first place is also something impossible to understand through intellectual thinking and budha said it is impossible to explain in words that, just like it is impossible to explain quantum phisics to a dog so you have to find that answer by yourself using the techniques you consider apropiate.
Although budhism is a system that has never been contradicted, proven illogical, disproved scientifically by nobody in 2500 years it has these 2 spots you touched (probably 3 do not remember exactly) that can be neither proven nor disproved intellectually, just like string theory. Sad but you have to live with it. The nice part is that it gives no importance to intellectual thinking and promises you to find out the answers by yourself using the techniques it teaches, that is the whole point.