In the link perkele provided above, the author says:
As the early Buddhist teachings freely admit, the predicament is that the cycle of birth, aging, and death is meaningless..."
If what's meant by "the cycle" above is a reference to one birth, a death, a rebirth and so on, over and over again -- with no memory from one life to the next of ever having lived another life, each life perceived as a single unit with no visible connection to what happened in a previous life, or what will happen in the next -- is that "cycle of birth, aging, and death" any more or less meaningful that the cycle of life, birth, aging, and death that we can know, and can see, right here, right now -- your life, my life, every single life -- each unit of life from birth to death?
I don't see that it makes any difference at all whether there is rebirth or there is not. Whichever is the case, there is still suffering, birth, aging, and death. Right now that is happening for me, and for you. A hundred years from now it will be happening for people we don't know. From where we stand here, it has no knowable beginning or end. Whether each individual here on earth now is one being who only had one life, or one being who has had thousands of lives and will keep on having them, the sum total of suffering in the world is EXACTLY THE SAME.
Escape from the cycle of life -- whether it is through our own death with no rebirth, or through a last life in which all becomes clear and we go to nirvana (what's nirvana after death? endless bliss? is that meaningful? or is it something else that we don't know the meaning of? making it, to us, meaningless) -- ending one life, or the last in a thousand lives, only ends birth, aging, and death for one being. There are still billions more individuals who will repeat the experiences. Whether you are reborn in a new life, or not, beings go on being born, and suffering continues.
There is no inherent meaning in rebirth; there is no inherent meaning in a life without rebirth. As the Buddha has often tried to point out to us, there is no inherent meaning in anything. We add our own meaning to life.
If a person suddenly feels down and depressed because they feel life is meaningless, here's the news: they are right, they are seeing the thing accurately. What they need to see next is that this is always true, and that meaning only comes to a life if the one living it provides that meaning. And each of us has the power to do that, but we have to know that's how it works, and choose to make it happen.
What I see is that the only thing that changes the sum total of suffering in the world is ourselves, using a viable system that does reduce suffering to reduce our suffering, and sharing that system with others so that they may do the same.
I choose to stand with the Buddha in deciding that reducing suffering -- not just for me but for all beings -- provides worthwhile meaning. Living my one life fully, in a way that is most beneficial to others now and in the future is the meaning I choose to give my life -- treasuring this opportunity I have to live, and seeing just how much I can do with the one life I am certain of. This is my Apannaka/Safe Bet: If I treat this life like it is the only one I will ever get, and the only chance I have to do something that helps others, clearly I will give it my all; if it turns out that there is a Cosmic Order that lets this life lead to another that gets its start based on what I put into my life, that being should have a great start; if the cosmic order comes with a balance sheet, surely I won't be found wanting for having given it my best shot.
I may never have as great a positive impact as I'd like, but I'm going to die trying.