Feel free to demonstrate the objective scientific point of transition from "not human" to "human". It doesn't, and can't, exist within the context of biology.
Therefore, if you don't accept that life begins at conception, there is no scientific point at which you can claim such a transition has happened for you -at all-, and logical consistency requires that you agree society should likewise be free to kill you at will.
Conception is a process. Biologically, there is no "moment of conception" as the Catholics like to pretend. Sometimes the egg implants first, sometimes the sperm fertilizes it first, and so on. There is no set order for all the various steps that take place during conception. (Some orderings have better success rates than others, but none have a 0% chance... Oh, and about 50% of all conceptions are spontaneously aborted without any human interference. Who should we blame those on?) It's impossible to say life begins at conception because it's impossible to say when conception begins.
In other words, you are completely correct. There is no exact transition point. Which means there is nothing to do other than make one up, as best as we can.
Can you pinpoint the exact moment that a child becomes an adult? If not, I guess all two year olds should have the right to vote, drive, drink alcohol, and serve in the military.