My view was that the way I interpreted Buddhism - it would not function without the doctrine of rebirth. Kamma teaches that each of our actions bears a kammic fruit at some point. This is fundamental to Buddhism because it constitutes Right View - a factor of the Noble Eightfold Path. However if your view of kamma is restricted to being limited to only one lifetime, then it becomes evident that the teaching starts to fall apart. Would it hold true that in the span of one lifetime all volitional actions would bear fruit? The killing of living beings is said to bear negative kammic fruit, this may not be the case if restricted to one lifetime. Take a man who works in a slaughter house, or a pest controller etc. Their actions may not bear fruit in this life time - our society does not punish people who kill for a living, they may lead this whole lifetime killing animals every day and not receive any real retribution for their actions before they reach the grave. I'm sure there might be other examples of this.
Kamma is also used as an explanation for where we are at in the present. This sense of kamma also starts to make less sense if you restrict it to only one lifetime. Say for example a child who is kidnapped and horrendously abused for years in captivity, what could they have possibly done within this one lifetime for this to be deemed the ripening of kammic fruits? This is usually where the past life kamma comes in, that this person had done something in a previous life which is bearing fruit in this life (a notion that I strongly disapprove of, for reasons I shall not go into now). If there is only one life - what can an innocent child possibly have done to deserve abuse or murder? Kamma, at least from the way I was taught it, fails as any kind of 'actions bearing fruit' doctrine if it is viewed as being restrained to a single lifetime. So in my view denial of rebirth leads to the failure of the system of kamma - which is defined as a requisite for Right View - which is a part of the core teachings.
I do not believe in rebirth, this means that I cannot accept the kammic teachings in the way that the Buddha intended them to be understood, which means I fall into the category of Wrong View, which presumably means I cannot attain Nibbana, without fulfilling the Eightfold Path. Conclusion: I am not a Buddhist.
"For me, it is far better to grasp the Universe as it really is than to persist in delusion, however satisfying and reassuring."