How do you propose people kill themselves? There are many ways to do it if you are strong enough, physically.
Taking an overdose is the obvious way. This runs the risk, depending on where you do it, of not being found until days or possibly weeks later in an advanced state of decomposition. This would clearly not cause any distress for the person(s) who find you, be that family, friend or police etc.
You could throw yourself off a tall building, risking serious injury or even death to anyone you may hit on landing, not to mention the enormous psychological damage to those who witness it. In addition you may survive the fall but be permanently brain damaged and/or physically disabled as a result.
Another popular option for suicide is standing, or driving, in front of a speeding train thus risking a derailment and injury or death to tens, if not hundreds, of passengers and crew and the psychological effect on the driver who now believes it is their fault that person is dead even though there was nothing they could have done to prevent it. In these cases if the train is still capable of running the driver has to be relieved at the next station and in many cases is so traumatised by what has happened they never drive again thus causing them and their family financial hardship.
How about throwing yourself off a bridge onto the road underneath, this has the huge potential to cause a multiple pile-up with more deaths and serious injuries to countless innocent road users.
Hanging is a good one and is generally successful but not so much fun for the child who comes home from school to find Mummy or Daddy dangling from the bannisters or for the dog walker who comes across a corpse hanging from a tree in the woods.
There are all sorts of ways to try to commit suicide, none of which are guaranteed to work, but are guaranteed to have a serious and terrible effect on third parties who unwittingly get caught up in it.
Does anyone really think that any of the above are preferable to AD or similar where you are in a safe place with professionals to assist and you are assured of a good end.
Before termination was legalised women were forced to go to back-street abortionists or try a bit of DIY. Many women bled to death or died from serious infections, also horrendous for the person who found them. I expect that similar arguments against abortion were raised as are being made against AD and that some women look on abortion as an extreme form of contraception or morning after pill, but is that a good enough reason to deny it to anyone who's own mental or physical health is at risk by continuing with the pregnancy?
Similarly with AD it should be available to anyone who needs it. Not all terminally ill people do need it, but it should be an option for anyone who's continued existence (not life, because they don't have a "life" anymore) has become unbearable.