Ms Davidson said her own experiences of IVF treatment and some of those close to her suffering from dementia had led to a change of heart on assisted dying.
In a column for the Sunday Telegraph, she said her decision to vote against the Bill is the one choice that "eats away" after her 10-year career at Holyrood.
She is due to step down as an MSP at the election next year and is expected to enter the House of Lords.
The Scottish Parliament has twice considered Bills aimed at introducing assisted suicide, with these having brought forward by independent MSP Margo MacDonald and - following her death from Parkinson's disease - Green MSP Patrick Harvie.
Both measures failed to get enough support from MSPs to become law.
Ms Davidson, the MSP for Edinburgh Central, said her decision to vote against the independent MSP's Bill left her "genuinely torn" and her experiences in life afterwards had led her to believe that people should have more control on end-of-life decisions.
Speaking about the process of IVF, she said: "The systems and processes of egg retrieval; choosing donors through any number of characteristics from height to family medical history; embryo implant and even being able to guarantee against twins, makes a mockery of the mystique of kismet surrounding birth.
"And if birth can be so demystified (for the over 50,000 people who undergo IVF treatments in the UK every single year) then what rule of fate exists for death and why is there such imbalance?"
Despite watching some of those close to her being "consumed" by dementia, she said she would only support assisted suicide for the terminally ill.
Ms Davidson said: "For me, a tortuous clash of head and heart, faith and intellect, right to life versus injustice of suffering was finally resolved by living the science of birth and watching the degeneration of mind, each day."
She continued: "In 10 years of elected politics, I have made more mistakes than I can ever hope to remember - some through overreach, some by omission, others by nothing more than blunder.
"But the mistake that eats away, demanding redress, is voting against assisted dying.
"Sometimes, amid complex arguments and conflicting evidence, you know - simply know in the essence of your being - that something is plain wrong.
"It's time to change the law."