Speaking as a biologist, sperm and eggs are alive even before they fuse. There's no scientifically meaningful way to specify when 'life starts'. So the question of when a developing foetus should be given the rights of a person is primarily philosophical.

I tried to avoid nitpicking by specifying that it's just a summary of the argument, but I failed. I should have used the term 'personhood' instead.

Science agrees with that assertion. The argument is over the more vague concept of "personhood".