This is one of those issues with no obvious right answer. It's almost more a question of faith, belief, or what have you.
A fertilized human ovum -- a zygote -- is the only substance on the planet that, if left alone, will turn into a human. (Reliable cloning is a ways off yet.) You can't say that about any other substance on the planet. Sure, it's just a mass of tissue, but it's a special mass of tissue unique from all other masses of tissue. To a mother (and father) that actually want a child, it's the most important mass of tissue on the planet. It's not a disease or a nuisance or an inconvenience, like having cancer. It's something that's supposed to happen as a naturally occurring result of sex -- which is a natural biological behavior of humans.
On the other hand, women are uniquely burdened by pregnancy. Obviously, there are health risks, and the HUGE majority of the world, even in places where abortions are illegal, makes an exception for saving the mother from death or serious disability. But women also face social consequences -- when you walk around with a fat baby belly, you have to deal with the way people treat you, which could be positive or negative, but still different than if you weren't pregnant. And physical consequences -- pregnancy and childbirth are hard on the body, even in cases when a woman isn't facing a serious medical risk.
And all of the financial, social, and professional restrictions -- once you have a child, you are legally responsible for that child, which means you have to pay for the child, sacrifice your social life and your professional advancement, and take care of the kid, to your own detriment, until it reaches the age of majority. Unless you give it up for adoption or it gets seized from you (and you get thrown in jail), both routes having significant emotional consequences.
I've always felt that, more important than any of the tangible consequences of abortion, is the intangible one: The right to decide whether or not to become a parent. Even if you give a child up for adoption, you've still reproduced. You're a parent. Interestingly, this right isn't just a female right -- men also become parents when a woman has a baby. There were some interesting U.S. court cases, after Roe and its progeny of later cases, dealing with in vitro fertilization. Situations where a couple going through the in vitro process gets divorced, the woman wants to implant the embryos, but the man wants them destroyed (or vice versa - the man wants kids through a surrogate but the woman doesn't want her unborn children being born). Those were some interesting reads, because the balancing of rights was a lot less obvious when the mother's body was taken out of the equation.
Nobody really knows when life begins. Obviously, if a woman in her 40th week is in labor, that child in her belly is alive. It didn't suddenly become alive when it was birthed. It didn't undergo any significant biological change. It just moved from one side of her birth canal to the other. If you stab it before it's halfway out, that's not an abortion, it's a murder.
But if you go back week 22 or so, very few babies can exist outside of the mother's body. They're essentially parasites. Around week 23, however, about a third of babies extracted from the mother live. By week 24, about half of them live. By week 26, about 90 percent of them live. Modern medicine is getting better at this, too (for good or ill).
Most people would pick the point of fetal viability (if it were a more definite and obvious target) as the bright line. A lot of laws that permit abortion before the third trimester but restrict or prohibit it afterward are a crude attempt at that.