When you're discussing abortion you're discussing several issues at once; hence most abortion debates are talking at cross purposes and frustrating all parties.
One aspect is legality. There are currently around 190,000 abortions in England and Wales per year (total population 56m). International statistics suggest that the number of abortions in a country doesn't depend on the legality there, although your chances of surviving do, as does female life expectancy more generally. Assisted suicide is currently illegal in the UK; if the illicit cases reached 3 cases per 1000 population per year, it's very likely it would get serious parliamentary debate time and at the very least some concessions and permitted circumstances.
You don't have to approve of a thing (eg smoking) to recognise that restricted legality of it could be a good idea. When abortions are legal, they are more likely to be sought early, and it should be obvious to anyone with half a brain that a 6w abortion is better for all parties than a 26w abortion. The neural column isn't closed at 6w, and the cervix doesn't need to dilate to let such a foetus through. This is the kind of thinking that keeps smoking legal but restricts sales to over 18s and in plain packaging behind closed cabinets.
Legality is a completely separate debate from ideas of morality, and separate again from philosophy.
Currently, artificially ending a pregnancy before around halfway through necessarily results in the death of the foetus. A woman who wants an abortion other than TFMR* is primarily concerned about the pregnancy, not the foetus. If science could transplant the foetus to another host or incubator or suspended animation of some kind to save for later, termination of pregnancy wouldn't mean termination of life. The only arguments against abortion which hold any water are those based on ending a life; if abortion didn't do that, there would remain no sane objection to it.
So abortion debates hinge on whether a woman's rights over her own body (the pregnancy) are more important than those of a not-yet-legal-person (the foetus). Currently, legally, a human becomes a legal entity at birth and ceases to be one at death - this is why the precise time of birth and death are so carefully recorded. Having a clear line is important for clarity and certainty. Changing the definition of legal personhood would have implications far beyond abortion, so although culturally there are varied grey areas, legally there are not.
And once you have established that question, there are two logical options. Either the legal person has greater rights, in which case her right to an abortion trumps the foetus's right to incubation and delivery, or the legal person has LESSER rights under law, which sets horrible precedent. We believe in equal rights for all humans nowadays, and the latter option is dangerously at odds with that. The law must uphold the notion that a legal person has rights to his or her own body which cannot be trumped by anybody else's rights. Our laws on assault including sexual assault rely on this first principle.
Nobody in the history of the world ever decided to get pregnant so they could have an abortion. Never ever. In debates the options are often presented as "don't get pregnant" v "have an abortion" whereas it's far too late. It's "stay pregnant" or "don't stay pregnant", and being pregnant is actually kind of a big deal physically and mentally, even if you want to be. It's far closer to the debates around programming self-driving cars, and whether they should be taught to sacrifice their passengers or bystanders when they judge there is no non-fatal way out.
Incidentally, contraception options are better in the UK than they have ever been. But there's an awful lot of sexually active people in the UK - even if we guess at a third of the population having straight sex that means 333 per thousand population, so 3.3 abortions per year per thousand population looks bloody close to the expected contraception failure rate, ie pretty bloody low.
Yes, morally, when you perform a termination of pregnancy you are ending a human life, albeit not a legal one. I can see why that's a huge deal for people - it's a massive deal for me too and I am daily thankful it's a decision I've never even had to consider. It just isn't as big a deal for me as maintaining the legal personhood of every woman on the planet.