I do not believe that rebirth does not occur, however currently I see no reasons to believe that it does. Just like the question of whether or not there was ever life on Mars. To say there definitely was given the level of evidence that we currently have would be foolish. But to say there definitely wasn't would also be foolish. We don't know, but we don't have a reason to assume there was and act accordingly.
Sure the Buddha himself is said to have spoken about rebirth. But he also said to not just believe everything he said just because he said it. We should find things out for ourselves.
The best evidence we have is reports of children having past life memories but these are shaky and not so convincing when we take a sceptical approach. Children are playful and highly imaginative they are also suggestable. If your kid sees a WW2 film about fighter pilots then starts playing and talking around being a fighter pilot it can be very easy to suggest your way towards being convinced they are acting out past life memories, especially if you already believe in it. Fanciful kids and incredulous parents is all you need. Get an "expert" in past life regression involved and you are well on your way to being totally convinced along with your child. It may be the case that children do sometimes recall past lives, but it could also be people putting thoughts into their kids head and spinning stories together.
As far as I am concerned what matters now is the present moment. Rebirth doesn't have any obvious bearing on that so its truth or falsehood are ultimately irrelevant.
"For me, it is far better to grasp the Universe as it really is than to persist in delusion, however satisfying and reassuring."